I don't have an answer to your question, but I can say that you should just go open a garbage throwaway bank account.
If you're in the midwest the name "TCF Bank" comes to mind. I abuse the heck out of them. I walk in there with several MO's from many different instituions and write my name in the "to" and "from" lines and just hand them over. If they have a problem with it, so what? There are tons of banks that I would rather do business with.
I doubt you can get a negative mark on Chex for depositing large amounts of MO's.