You are late for booking June. In addition, sometimes the hotels put minimum stay requirements.

I’m not sure that will help for June but try searching for 6 nights. If you have the points, or are globalist and can do a points advance, book the 6 nights and then cut back.

As for chances l, what are the odds you would cancel a June trip in January? Then multiply that by the number of base rooms you guess there are booked on your days and you have an answer. (Admittedly not an easy number to know).

Use something like open hotel alert to search for newly available rooms in the base room category.