a term meaning, literally "ten thousand years", with an implied "may you live" stuck in there somewhere

Makes the Polish toast Sto lat, "may you live a hundred years", look pretty tame.

I still like it, though, especially if you add an implied "..in one night" at the end.

Incidentally, I just read that "Banzai" is traditionally repeated three times. Surprisingly similar to our "Three Cheers" isn't it? With the difference that we don't actually repeat "hooray" three times.