Have you tried calling either HGP or the hotel itself to ask whether they can combine all of the reservations into a single reservation with different rates?

If this doesn't work, I'd at least contact the hotel about a day before arrival to tell them that you have a bunch of consecutive reservations and want to keep the same room throughout, assuming that you've booked the same room type. Remind them again when you check out. You shouldn't have to pack up and change rooms during your stay.