Wow - that's definitely far beyond what most PM's offer.

I'm wanting to offer my guests a discount for extending their stay, or coming in a day earlier, to help cover one night gaps in my calendar.

Hopefully your insurance policy also compensates you for loss of use - where it continues to provide you your rental income.  

I would offer the tenant this.

The only issue I think you could be facing by renting it like that is when it comes to insurance. 

I had walked the property and told him he was crazy for not making an offer.

Maybe your offer will be more attractive to others.I'm not poo-pooing your idea, but I am skeptical enough that I won't ask for an analysis of a particular market. 

If your lender offers the program they should be certified or trained in some way on the program and can answer any questions you have on it.

Will partly compensate you mortgage and insurance, and you can put you rents to take care of rest.

(We were planning to move back to our rental and rent our primary due to higher rents so started to rehab the primary then found out insurance would not insure us due to the high fire risks if we changed so ended up rehabbing both houses and burned the savings).Our dilema is we don’t want to sell either of our current houses due to excellent locations and appreciation potential but want to progress with more rentals.