-Maximum number of internal links on a page

Depending on how powerful your site is, I would suggest keeping it around the 100 links mark per inventory pages; at least initially.  If you offer the ability to see more products at once that will keep all of your customers happy.  However, the fewer links per page, the more power you send down to your product pages.  If you start building links to these product pages, though, that could become irrelevant - depending on competition.  If you still need to give extra boost to specific products, look for ways to link them internally from other pages.

-If Google frowns on really long category pages

From what I read, Google doesn't really consider the navigation pages to be very valuable content.  However, I would only be concerned with that if you were trying to rank your search pages.  So, I would focus on what your potential customers would want.  If you feel like you need to rank for a specific phrase, generate a landing page that leads into that specific inventory search.

-Anything else

I would suggest testing multiple designs.  It's easy for us to tell you what you should do, but it's better to hear it from your visitors.  Also, don't spend a lot of effort trying to get a specific search to rank, instead create a landing page for that product category, which will then lead into your search.  You will have a lot of unique content on there, and your customers expect to see a landing page.

I've talked to a couple people that have said that 301's will pass on the penalty.  A better alternative would be to try move the links over to your new website in waves.  If you experience a drop, then you know the link exists in that group.  Just do some quick checks on their domain, and see what you find.

Of course, if you are working with 10,000+ links, your batches are going to have to be pretty large.

Then again, if you don't have more than a couple hundred, go through the various domains, and try to identify problematic links.

How's your internal linking structure?

Do a site: domain.com check to see how Google perceives your internal linking.  Are your relevant pages on the first page of your site search?  If not, you may have an internal linking problem.

To check this I used a web based program to find all the outbound internal links of each page on my website (only 200 pages).  I then transferred this data into Excel where I sorted it by page.  From here I was able to see that my most important pages had 20 less links than the unimportant pages in front of it. I then went through my website adding additional links to my important pages, using the same keywords I was trying to rank them for, until they had the most internal links pointing at them.

Internal linking is typically a problem with websites that didn't plan ahead for SEO.