Give the notice! I'm on the other side and BH keeps telling me that they "think" they have a spot in August but since current families only have to give a 30 day notice they can't promise for sure.

We are moving into the area and gave our notice to our current daycare about 60 days out and after their first "sad to see you go" they haven't mentioned it and I don't see any difference in the treatment. I mentioned it to them earlier than I had to because I didn't want them to start planning the transition to the next room.
Maybe you'll give your notice and I'll be the one getting the long awaited call that they have a spot!