Keep checking yourself, as often as you're able to. And decide if you want to take a chance and book 1 or 2 nights if they become available. You then might be able to add on a night at a time. Sometimes that's too risky or nerve wracking or time consuming, but if your current reservation is off-site, you may choose to keep that entire reservation intact until all 4 nights might open up and then cancel the off-site.
Unfortunately, you might not be able to get even 1 night, so it's great that you have back up plans. BLT is very popular. Hope you have a fantastic trip!
Good luck!