Sounds pretty frustrating to me! :)
I've done this a couple of times, where I just couldn't use the Migration Wizard.
All the data you can get out of Sitefinity through the API. What I've done:
- Created custom tables inside the old Sitefinity website
- Used some code to get the data (News, Blogs or whatever) out of the CMS into that custom tables
- Created code from my new website to import it again into the right modules
Probably some things could have been more optimized, but you know how it works when you don't have time, or didn't calculated a non-working Migration Tool ;)
You also could try to create a repository with some methods that get the data out of the CMS and expose them through the WebAPI. That way you don't need that custom tables.
Another way would be to try to change the connection string of the providers inside a new 3.7 website, so that you can use the Migration Wizard to at least import the most basic stuff like news, blogs, libraries.
If you need detailed information, I maybe can help you.