Thanks, Nate... That's exactly the line of thought that I was running, between both jobs, hard to get on here as often...
I experienced this with my Reliant, and as well with my brother's Grand Waggy, it's carb-related for sure, as was posted... Reliant needed a carb rebuild. Grand Waggy needed a good healthy blow-off-your-eyebrows blast of carb cleaner. Unfortunately, I do not know that much about carburetors, have not yet had the joy of pulling one out and tinkering with it on the bench, so all I can tell you is that your carb is unhappy, and needs cleaning, if it's all gunked up, these problems arise, and the fuel efficiency suffers... There are, I believe, ways to tune the carb, but again, I do not know...
With the Reliant, feeding it premium helped a lot with the problem till the carb was repaired. When it was dieseling, pushing the gas pedal to the floor AFTER the engine was turned off usually made it stop, otherwise it would sit there and chug for up to 2 minutes...