In my case, the tenants who want to pay cash came with our latest 4-plex.
Since my last post, I've found two companies so far that don't require a minimum number of rental units and that can accommodate cash payments. One of them explained to me that they work with MoneyGram stores where tenants can pay their rent and the associated fee in cash if they like and that MoneyGram will then initiate the ACH transaction which will ultimately land in my bank account.
The guy who shared the above info with me was with RentPayment.com. Obviously, I have no idea at this point if their service is bad, good, or somewhere in between or if they're better than any of their competitors, but, unless I hear something that makes me go in a different direction, I'll probably give them a try.