There's not much to cover that everyone else hasn't except to emphasize that you need to fix your 12V problem before you try to troubleshoot any further. I have an '84 Allegro and learned early on that:
1) Power converters of that vintage suck
2) Power converters of that vintage suck even more when you are using it to charge batteries that have deteriorated beyond charging
I replaced my power converter with a modern unit with a smart-charging algorithm and 2, new 12V deep cycle batteries. The difference is like night and day - everything started working properly.
With regard to your generator, I would try the Seafoam first. If that doesn't work try the more aggressive carb disassembly and cleaning. Mine ran okay, but surged under a load. Seafoam made a world of difference. My experience with engines that sit, however, has been that if you need to choke them to keep them running then you have a blockage somewhere - probably in the jet that someone else mentioned. The problem is that there isn't enough fuel for the engine to run with the unchoked airflow.
