Try the Jackson House in Dune Allen Beach. The VRBO calendar is still showing availability throughout June. I've never stayed there myself, but it is on the same strip of beach where my family usually rents. It is fairly new 4 br/4 ba. It is Gulf Front so you have great views from the balcony and you are sitting directly on the beach. It is close to Grayton and The Red Bar. Also, close to the Silver Sands Outlet mall.
Jackson House
If you want a 3 bedroom for almost $1000 less I have the place next to Jackson House booked for June 10 - 17, Whispering Sands. I'm currently looking for someone to take my spot so I can get a 2 bedroom unit that just opened up in the same complex where my other family members already have 3 units. I don't want to lose my Whispering Sands deposit so I can't change plans unless I have someone to take over. PM me if you are interested in Whispering Sands for June 10-17. It's a first floor, newly renovated 3 bd/2 ba, 1300 sq. ft.
Whispering Sands.
Otherwise, the Jacskon House looks pretty nice to me. I know the Dune Allen area and is a great beach location.