There are a few related threads here that suggest that leaving after the 3rd day is probably not a great idea (sadly), after 4 you could probably get away with it, but the chances of nobody checking and you being able to do online check-out are lower:
Early Departure Charge
Leaving 1 night Early (on a long-term/7 day min) & Checking into a New Hotel

Sadly I can't think of anything to do beyond:
1. Cancel and hope the room comes available again and rebook (risky, but may work)
2. Trying to call and seeing if the agent is a bit better, but I think the live agents can see the same availability: Likely you can double check on the hotel's website and see if one of the other rooms that is available may meet your needs
3. Doing (#1) but with a cash booking made as a backup

Obviously ideally the hotel would do something, and they could if this was a cash booking - but they can't do reward bookings.