I booked directly through the hotel through my TA to avoid this sort of thing. It was not enough notice for my guests and I simply would not do this. My TA isn't making as much money doing it this way, but frankly I don't care. I thought it was wrong to give people less than a month to decided what they wanted to do and get the $ together. Booking with the hotel, we got a block of rooms that were released 45 days prior to the wedding, but people could book at that price at the last minute if needed.
Get rid of the 3rd party, it's only hurting you and helping the TA, it's your wedding. Furthermore, I would drop this company all together. They sound terrible.