Rob, don't ever listen to Uncle Phil, he's full of IT! (Not really, but...) I never remove the tank to pull the carbs. And, I never loosen the clamp screws to pull the carbs either. A short lever under the edge of the carb caps on both sides will pull them loose of the boots. Ya gotta loosen the clamps and do a couple other things to reinstall, but not to remove'em. Trust me, I did it a half dozen times just last week.
Spark, air, fuel. You've got spark or it wouldn't go at all. Air? Good question, how's the filter? Could be a rat's nest in there. Really, I've seen it. Fuel? Most likely the problem. For the best carb analysis, go to ST-Riders.net and access the carb rebuild thread. It is very thorough, yet doesn't require a complete disassembly. This thread is in the public area so you should be able to see it, but I recommend subscribing. Don runs a great site, and it's the hiSToric successor to the original ST e-mail site.
http://www.st-riders.net/index.php?topic=10249.msg89666#msg89666
I'm suffering a similar but not so severe issue with my old 91, recent run yielded only 35 MPG after a complete carb swap with known good carbs. There's another issue on mine I have yet to analyze, but it ain't carbs.
Good luck and keep us poSTed,