It seems to me that I am in a tight spot.

I explain that with traffic in our area there is no easy way for cleaners to rearrange the pre-set schedule for the day and they have a tight timeline AND that good cleaners are extremely difficult to find and they work very hard.

If you haven't spoken to RTB already, I'd suggest you phone them and see what they say about the situation.If the tenants threaten to move out I would be inclined to let them go - the rental market is tight right now and, based on their lack of awareness about household issues, they may very well cost you more money down the road from some other issue.

Check your local statutes because there can be some deadlines you don't want to miss.

If you miss the deadline, the tenant can sue you for double the security deposit amount and attorneys fees EVEN IF they were clearly in rent payment default and are being evicted.Only an Alabama licensed attorney can appear in court to represent another person or entity, unless it is small claims court. 

Confirm the bank info with them and give them a hard deadline to pay you the money.

This would be the same as FHA, but with not as many restrictions (Like PMI the life of the loan) You would probably be tight either way with 5% down & closing costs, but it still may work.Other more doable option would be to find a like minded partner & partner up with them!

Lock it down tight as you can.

@Devante Henry, looks a little tight for my taste but everyone has their own risk tolerance. 

This would leave a tight profit margin on rent and at the current interest rate I would net 200-300 dollars a month after mortgage, HOA, Taxes, Insurance.