But thanks to a suggestion from Frenkel (who pointed out that Monster Bash has hidden cheats too), I think I'm on to something now:
Unfortunately it looks like the code to activate the cheats has been removed from the .exe, so the only way to get to the cheats is with hex editing. In this case I changed the bytes at offset 0x172A0 from F0 E0 to E7 E8, which changes the purpose of the F10 key so that instead of showing the hints for the level, it brings up the warp cheat. It'll have to do until I figure something more out.
There's some curious code in the .exe to do with activating something too. It checks the system date and will prompt for a code if the year is before 1992, and the code you have to enter in is some mathematical variation on the date (like it's the year divided by two plus the month or something.)
I'm still not sure what that's for, but like the warp cheat it seems that there's no code to call that function either.

