Here's the concept at its core: how can Google crawl redirects and index new pages if it can't crawl those redirects to get to the new pages and process the 301s?

Fix that to fix your problem. The link I shared has a lot of good comments very centered on this general topic.

And, I am intentionally avoiding giving an absolute solution to you because, quite frankly, I don't know enough or am involved at all in your site to feel comfortable doing so. Strategically, I'm happy to share ideas/best practices.

I think I get what you mean and this stuff can get a bit tricky - first and foremost, it can take days/weeks/months to get things unclogged after an issue like this and there's no promise you'll get exactly the same ranking as you had before.

Getting back to your original question, and not to kick you when you are down, however, Google never recommends moving an entire site at once because you don't catch major things like this. Now, to your question, here's answer: "In order for Google to index your new site it has to re-crawl the old site which is redirected there. As each url is accessed, the redirection is found and applied." I think that's what you are trying to get at?

There's more info here that may be worth you reading through:  http://googlewebmastercentral.blogspot.com/2008/04/best-practices-when-moving-your-site.html

To your point about a new domain - new domains aren't given as much validity as old ones, which can mean you have to do some rebuilding and re-earn rankings. If the goal was to get rid of old, bad link juice, what have you done to drive new links to your new domain (and PRWeb does not count in any way - it's a scam, IMHO)? That's another factor that could impact a positive improvement.

At the same time, I may not have read as closely as I could have, but how could you do 1:1 redirects from the old site to the new and yet offered up a 404 page to direct people from the old domain to the new? Was there a specific reason why you didn't want to 301 from the old main domain URL to the new one?

Yes, it's normal to see a drop and this all takes time to recoup. It's the trade off you made when you opted to start from scratch, unfortunately. The other thing is, there could be issues going on with the site that aren't related to spammy links - I don't know enough about your site to speak to specifics, but it's another possibility that something else could be wonky.

I agree with Sebastian's follow up suggestions. It's way quicker to de-index yourself than it is to get those rankings back. Even one the robots is "cleared" it can take time to get back to where you were.

If they can't track their current site, then you are right, they don't care enough. Good thing they can't get what they want, because if it were that easy to de-list a site without having any back end access to it,  then competitors would be doing it to each other non-stop.

If they refuse to make contact then they get to have everything working against them. If you can make contact, then the action items Matt suggested are the next steps.

Good luck with them as a client

A slightly different way to look at it/somethings to consider: I wouldn't advocate trying to manage two sites as well as competing with competitors. Now, that's my business choice because the possible mess of the back end management/resources/content/marketing and everything to keep both sites viable and performing well. I wouldn't have the resources.

As a user, if I were researching, I'd also possibly get confused or feel slightly disconcerned if  I came across both and found out it was really the same company. Also why I wouldn't advocate for it.

That said, any move can cause a possible dip in rankings and performance. That's just a risk. After an initial dip, if the CMS is better, than the site performance could be way better than what you had before. I can see why companies don't want to risk it, though. Money is money.

Ultimately, there's the decision that's best for you, with everything you mention and what George mentions, as part of your consideration.