This may be a good start. 

I always say, no good deed goes unpunished; meaning “letting” tenants just move a few things in, now makes you liable for their belongings if something were to happen i.e. flood, robbery, fire etc… AND those things can and do happen, then their renters insurance probably doesn’t start until the 1st of September and you said their lease doesn’t start until the 1st of September.Do the right thing, refund back the previous tenant IF the new tenants move in early, and also change the lease date and the new tenants need to pay from that date.

Is this legal and a good idea? 

Good for you for creating a win-win situation! 

Obviously there's a lot I don't know about your deal, but using napkin math and your figures, Id go for it - I think $1600-1800/month is realistic depending on the area at that valuation (just guesstimating the neighborhood quality based on ARV).

I thought the seller and buyers broker split the commission.It is a new way of framing the agency relationship as of 1/1/24 due to the changes happening nationwide.In practice, most sellers are still paying buyer agent commissions as it is a good business decision to do so. 

Good luck!

Sounds good.

It is a good way to drive 5 star reviews.

This is some very good perspective and I really appreciate the insight!