I agree that you have to spend the time travelling the Beartooth, but you could spend your last night in Yellowstone at [or near to ] Tower, Roosevelt Lodge I think is one option, or you could even make your way to Silver Gate/ Cooke City and start your journey from there. You really need to book Yellowstone lodgings asap as it's possible it could already be too late for August, but if they are booked keep checking back for cancellations. As Yellowstone is so big it is better to book lodgings in different areas in my opinion, say a couple of nights in Grant village and a couple at Canyon and then maybe the last as mentioned above.