You may want to watch this Google hangout: http://www.youtube.com/watch?v=7NNf_AhA1gw&feature=share&t=42m25s (42:25).  The question is exactly what you are asking.  John Mueller says that if you are showing Googlebot your full content but users can only see it by logging in then that is cloaking and is against the Google guidelines.  If you show a snippet of your page to users and Google sees the same snippet then that's ok.  He said another possibility is to use "first link free" where you allow the user to see a limited amount of content and then put the rest behind a paywall or other type of a read gate.

I'm also in agreement with Egol in the fact that putting content behind a read gate could really turn away users.  I hate it when I search for something and find what looks to be the perfect answer to my question only to find that it's behind a gate.  The result of this is that I immediately click away.  And, for sites that I know regularly have gated content, I won't click on them at all in the search results.  If this type of user behavior happens often then there's a good chance that it will be seen as a sign of low quality and the Panda algorithm will affect your site which could result in drastic drops in rankings across the board.

It's not possible to remove a Penguin issue in 3 days even if you have managed to get Google to crawl and disavow all of the links on your disavow file.  This is because you won't be able to escape Penguin until Google refreshes the Penguin algorithm.  AND...in order to see a dramatic recovery like the Link Detox graph shows, you'd have to have a site that has a really good base of good links underneath the low quality links.  Most sites with Penguin issues will not see a dramatic recovery...and if they do, again, it would almost always be on the date of a Penguin refresh.

However, the Link Detox tool is describing a manual penalty, not Penguin.  (However, they're a bit misleading saying it "speeds up recovery from a Google Penalty".  Officially Google will tell you that Penguin is not a penalty, but simply an algorithmic change, but most webmasters would tell you that Penguin is a penalty.)

If it's a manual penalty, then you don't need to have the links in your disavow file crawled in order to lift your penalty and if this is the case then the "boost" that they are talking about won't really help get a penalty lifted. Within 24 hours of filing your disavow, the webspam team is able to see what is in the file.  When they review your request for reconsideration, they check to see if you have disavowed the right links.  It doesn't matter if those links have not been visited and thus disavowed yet.

Is it possible to lift a manual penalty in 3 days like Link Detox's website suggests?  Yes.  I've had it done.  We once filed for reconsideration and three days later we had a response saying that our penalty was revoked.  But, out of the hundreds of requests that I have filed, I've only ever once had Google respond that quickly.  Most requests are taking 4 weeks to get a response back right now.  Is it possible to have such a dramatic recovery as the graph shows?  Yes, if you have a sitewide manual penalty and your penalty gets lifted, AND you have a good base of natural links then some sites can show a dramatic improvement.  But, again, it has nothing to do with getting your disavowed links crawled faster.

I think that tools like Link Detox can have some value in helping site owners (but as I have always said, they don't replace the need for a manual audit.)  But, I have to say that I am concerned about the way that they're marketing this tool.  I think there could be some value, if you have a Penguin hit site, in getting your disavowed links crawled faster.  It's conceivably possible that if you didn't, then Penguin could refresh and your disavowed urls have not been visited and therefore are not disavowed.  But, the way that they've marketed it it sounds like any site that uses this tool can have top rankings again within 3 days of using it and that's quite misleading.

It really depends on what you mean by "take effect".  As soon as you submit the disavow, Google starts applying an invisible nofollow tag to each link that you have in that file as they crawl the web.  However, in some cases, it can take 6 months or more for all of the links to get crawled.

Will you see a change in rankings after you file a disavow?  I have seen some sites where within 24-48 hours there is an improvement which is always nice.  However, if you were affected by the Penguin algorithm then you won't see any improvement until Google refreshes Penguin which could be any day now or even months from now.  AND, in order to see improvement you have to have good links present.  If your previous rankings were there because of links that are now deemed unnatural, then there may be no improvement at all either now or when Penguin refreshes.

A lot of sites saw a drop in mid November but there was no announced update.  You can read a good discussion of what some site owners saw in the comments on this post:

http://www.seroundtable.com/google-update-nov15-17689.html

My gut instinct is that this was a refresh of the Panda algorithm, but Google no longer announces these refreshes so no one can know for sure.

But, there really isn't an easy answer to your question as there isn't an obvious solution.

I would disavow the blogspot subdomains individually.  So you'd have 1000 lines that say:

domain:subdomain-name.blogspot.com

The documentation for the disavow tool (http://googlewebmastercentral.blogspot.ca/2012/10/a-new-tool-to-disavow-links.html) says the following:

Q: Can I disavow something.example.com to ignore only links from that subdomain?
A: For the most part, yes. For most well-known freehosts (e.g. wordpress.com, blogspot.com, tumblr.com, and many others), disavowing "domain:something.example.com" will disavow links only from that subdomain. If a freehost is very new or rare, we may interpret this as a request to disavow all links from the entire domain. But if you list a subdomain, most of the time we will be able to ignore links only from that subdomain.

What we don't know, however, is if we can do a disavow:blogspot.com to get everything from blogspot.  I wouldn't trust it to do this and I would definitely disavow each individual subdomain.

If you don't have a manual penalty then there is no way to upload anything other than your disavow file to Google.  Your disavow file is not read by a human.  It is machine processed.  You simply need to trust that you have done a thorough job and then, when Penguin refreshes, if you've got a good base of good links you should see an improvement.

Does your analytics data go back as October 3?  If the drop happened October 4, then I would indeed be worried about Penguin.

Have you been building links to this page?  More specifically, have you built keyword rich anchors to this page?

Do you see any manual spam actions in webmaster tools? (WMT --> Search Traffic --> Manual Actions)

I definitely agree that Penguin is a huge possibility.  But, I think it could be dangerous advice to send a site owner on a link removal/disavow mission when we don't know for sure.  There are many other possibilities.  It could be a Panda issue.  It could be that it was a new site and the previous high rankings were a honeymoon effect.  It could be that the /home.html page is blocked by robots.txt or has a canonical tag that is confusing Google.  It could be that they changed the title tag on the page so that it is no longer appropriate.  It could be that the site was hit with malware and users are clicking away because of virus warnings.

(btw...the thumb down was not from me.  I respect that you are trying to help but just wanted to comment to make sure that the site owner (or someone else reading this post) doesn't go off disavowing links without getting to the cause of the problem first.)

Absolutely do the disavow first.  There's no reason not to, especially if you are dealing with an algorithmic issue.  (For some sites with manual penalties, I'll submit a disavow as soon as I can and then do the outreach.)

On a side note, if you have an algorithmic issue (i.e. Penguin), no one knows for sure whether you even need to remove links.  Of course, there are benefits to removing links.  Google will tell you to do so because you don't want people to look at your site's links and see bad ones online.  But, I recently asked John Mueller in a hangout whether link removal (as opposed to disavow) was necessary for Penguin and here's what he said:

From a theoretical point of view, using the disavow tool is enough...from a practical point of view it almost always makes sense to still delete those links as much as possible.

You can see the response here at about 41:20: http://www.youtube.com/watch?v=KWYooFjmx5c&list=UUthrUiuJUtFSXBUp48D8bAA&index=2

The main reason why removing may be better than disavowing is because it can take weeks or months for a site on your disavow list to get recrawled and as such be disavowed.  However, I have found that in most cases, if you have spammy links, if you don't control the login info you used for link submission (or if there is no way for you to remove the link yourself) the response rate is always very poor (like 10-15% if you're lucky).

If you've been hit by Penguin, there are two things that need to be in place in order to recover:

1. An EXTREMELY thorough link audit and disavow.  IMO it's not enough to get 80-90% of the bad links.  The only sites I have seen recover had close to 100% disavowed.  This means doing a manual review of every single domain linking to you from every source you can find.

2. A site that has a base of good natural links with the ability to attract new links.  If you don't have that and you are planning on manufacturing your own links again then you probably will not recover.

While it could be Penguin, I don't think we can make that call on the data given to us in the question.

Take a look at your organic traffic only.  If you use Google analytics, go to Aquisition --> All Traffic, then choose google/organic.  Can you tell what date the drop happened on or started on?

Now go to Behavior --> Site Content --> Landing pages and click on each of the top pages.  Is there an obvious drop for each page or just the home page?

How old is the site?

Can I ask why you did the 301 from domain.com to domain.com/home.html?  Is there any chance that the /home.html page has either a noindex tag or is blocked by robots.txt?  Is there a canonical tag on the /home.html page?  If so, what does it say?