The elevator theme is the "BGM 10" I'm talking about in
post #23 in this thread. The Capcom Wikia credits that to Yasuaki Fujita on account of it being a "sister track" to arcade stage 4-1, which sounds to me like it's a total guess.
The only track Fujita talks about is 4-1, and he didn't indicate that he wrote anything else for the game. That's not to say he didn't: he could have omitted it or just forgotten. But the one theme is all he's talked about and I haven't seen any evidence suggesting he did anything else.