The short answer as far as I'm aware (and I've been following Pinax development for some time now) is that there is no straightforward path to upgrade the project from 0.5.1 to 0.7beta3. I'm not sure how familiar you are with the code, but this is the process I would use based on my limited experience:
Start by using the social_project/ that ships with the latest version of Pinax. Copy into it any changes you made to the settings.py file as well as any custom apps you have.
The templates and media have moved to folders outside of the projects, but if you customized any of them (I'm sure you did) take the custom ones and drop them into the template folders in your project to override those in the default theme folders. You should compare them to those in the theme folders to see what changes may need to be made to keep up with changes in the apps.
The next step would be to do the same thing with urls.py copying any customizations over the one provided by the project.
Try getting it running at this point with a fresh DB. Hopefully any errors will point you in the right direction to stuff that you might have missed or not known about.
Once you gotten it running most of the DB tables should be the same (I believe) except as you mentioned the Tribes stuff. Migrating the data, though, is still beyond what I've had to deal with.
Disclaimer: I've been following development but never had to perform an upgrade quite this big. Good luck and (obviously) back up your work and data before trying to port it all over.
See the documentation and code ( http://github.com/pinax/pinax/tree/master ) for more details. The code is a convenient (though tedious) way to watch the evolution between 0.5.1 and 0.7beta3, for what that's worth.