The gas cap would work. If the tank is vacuuming it'll also cause your fuel pump to run weak.

The fuel tank has three fuel hose connections. One for the fuel feed, one for the return and one to vent the tank. The vent line, I believe, goes to the Check & Cut valve then a small hose goes into a hole in the frame to vent. Someone correct me if I am wrong. Incidentally, I pulled the connections out of my fuel tank and they were so gummed up with fuel that they could hardly let any fuel through at all.

The charcoal canister also has a filtered opening on the bottom. I would check that. Just blow low pressure compressed air in the openings on top.

There is a fuel quantity test listed in the manual. Might want to make sure you are meeting that expected quantity.

Good luck!

Another update. The gas cap was apparently not actually vented. Leaving the cap slightly open works well though. Removed rat's nest, air pump, and associated items and everything is running pretty good. There's still a bit of hesitation at high rpm and I can't exceed 5500 rpm while in gear. I don't have any vacuum leaks that I can find. I do have an exhaust leak pre-cat that I'm told will cause it to run rich.