Well, that's two people who seem to believe it's my fuel tank.

So am I safe to assume that I properly pinned it on the tank, or could there be something more sinister at work here?

One thing I forgot to mention: after the first couple of stalls I realized that while approaching a stop, if I slipped it into neutral and gave it a "little more gas" I could keep it from stalling. Does this sound consistent with the diagnosis?