Bájate de la mula does exist - http://www.universalia.usb.ve/ediciones_anteriores/anteriores/universalia20/dime_quien.html
It is also mentioned here: http://www.word-detective.com/2008/08/moolah/
Venezuela in the thirties was full of Americans with a smattering of Spanish working in the oil industry. I think it's quite likely that they picked up the association between mula (moola) and paying up.
As I said before, moll óir means a pile of gold and is actually found in texts like folktales, though only rarely. It is not a common expression. The problem to me is that moll óir is pronounced mollore, so I see no reason why it wouldn't become mullore or mallore or something like that instead of moola. Why would it become moola? I take your point about this being one suggested origin, but we need to remember that Cassidy never got it right about anything. He didn't know any Irish at all. Moll óir is actually considerably better than his usual standard, as it can be proven to have been used by Irish speakers, but it still isn't a likely candidate by any stretch of the imagination.