I don't see the need for Samui and Phuket on the same trip..... if you are going to fly 7000 miles from east coast of America to Thailand you don't need to spend 9 nights on a beach.
Extend your time in Northern Thailand and see some more of culture, countryside etc
or even go into Cambodia and enjoy Angkor.

I also don't see why you are hung up on the min stay in Bangkok. Just book and pay for the 4 nights and stay 3. Or search out another hotel.
Rosewood Bangkok is the one to watch now. Heck even Peninsula or Shangri-la will provide an above average stay. Maybe not MOBKK level, but still, if you don't want the 4 nights these are the compromises