Solved the problem. I tore the bike apart and got to the fuel pump/filter assembly (stored right in front of the battery box, which is a pain to remove in and of itself). I took the pump off and hooked up the leads directly to a battery, at which point it ran, so it wasn't getting power when installed, evidently. I believe the pump is on its way out (I'll test it more this weekend) because months ago the bike took a long time to warm up and would cut out fairly frequently. I had read on VTX forums of a handful of people who have had their pump die and, not wanting to spend $100 on a new one, I was looking for a way around it.
I decided to run a line directly from the petcock to the carb. I spliced some fuel lines that I had removed and added the inline filter, and now it runs great. The only trick is that, since my petcock doesn't have a vacuum line, I need to shut off the fuel whenever I park the bike. This could be resolved by buying a newer VTX petcock which does have a vacuum line but until then, I'm fine with just shutting off the fuel manually.