I don't now if Jakes ever waivers on their rates even with a walk in. You may try Sunset Resort - I have never stayed there but have walked through it - very nice. You may also like Katamah - it is new (looks pretty neat) - if you look at trip advisor there are some very recent reviews of Katamah - I see the Laila room has an advertised rate of $100 in the summer - looks like it has a private ocean view patio. Treasure Beach hotel always looks interesting, but we have had lunch there and there has never been another person around - could just be our timing too. The grounds are beautiful though, so it may be an option too. I would think you would find one of them to give you a deal in June as I don't think it is very busy that time of year. You could always contact them now and see if you can work out something.