Lake island - Labor day permits

Hi,

does anybody have a suggestion for some camping spot that might still be available on a lake island anywhere in the ADKs for labor day? Popular spots like Saranac are of course not available on http://ift.tt/RsBsuw.

I'd like to rent a couple of canoes with a party of 4 and spend a night anywhere either the 3th or the 4th.

Thanks!