Thought I'd post the results of my call with Priceline...
Priceline was flat-out unwilling to do anything for me, even after escalating to a supervisor and offering to book another room & car rental.
I then decided to phone the hotel directly. They first told me to call Priceline as they couldn't do anything for me, but when pressed that all I was looking for was permission to cancel the booking, I was told that they would be willing to accept their regular cancellation fee which amounted to 1 night + tax. She gave me her name and extension and told me call Priceline back.
Called Priceline back and they were more than happy to call the hotel and confirm the cancellation fee.
After confirming everything, I asked if they would be willing to now waive the fee if I committed to booking two rooms for those same dates at a different hotel. They weren't interested, and that was that. I told them I would book through a different site.