Wow penalty fee that stinks. I had the same issue but My TA didn't give me the option of keeping the block of rooms for a fee but I'm also a Mexico bride so maybe they do things different. I asked my TA if she could hold the rooms until the end of the week, which she agreed to and then my FI and I sent out mass text messages and emails telling people if the plan on coming they need to book or else
I sent out 150 invites at the end of April w a June 3rd RSVP date and I only got half of my rsvps bak so I figured the rest of the people were no's and we called all the "probablies". Maybe your TA can stall just a few days to give you time to figure something out.