You'll be lucky to get any reservation at Hilton Head in June. We tried one year for a five day. Started right at 7 month window. Only got 2 nights. Got a 3rd night about 60 days out. Never got any more. This was for 2nd week of June.
I would call right away and get on the waitlist. We booked cash with the 25% discount for June 24 and 25 and we were just informed on Friday that we got June 26 - 30 through the waitlist. Sorry.