Update...
This Sea Foam stuff seems to be pretty good. Once I got it started again, it blew a ton of white smoke, but then settled into a good RPM. It stayed there for close to ten minutes before its first load-down, in which it blew more white smoke. Now the load-downs are only happening about every 5-6 minutes instead of every 90 seconds, and there's no black smoke... instead it's white, but not as bad. And the load-down isn't as severe either.
The gallon of gas is almost done. I think when it is, I will reconnect the regular fuel hose and plan on dumping at least one more full can of Sea Foam into the gas tank (which has 10 gal of fresh gas in it). This may just keep me from having to pull the carb!
I'll keep everybody posted. Thanks for the tips!