So what you want is if someone is a member of a group you’ll change home to the category associated with that group? The theme component that I developed is a good start for doing that, however, it appears that it’s broken. Right now, I’m the only one using it (I mean, I am the only user, so not even more users than me are using it on my site), so it’s not been a priority to fix it.
If it worked, it would apply the home url override only for members of a group, so it should be reasonably easy to modify it to support multiple groups and home pages, given that it’s easy to resolve whatever the problem is. 
If you’ve got a budget, feel free to contact me or post in Marketplace.