Thanks for the suggestions, everyone. We actually missed a lot of these because we left for the Marina early this morning.
We took a suggestion from the Boat US article that was linked and stopped at Defender for some Northstar Un-hesive (the two West Marine
stores near the marina didn't have Debond in stock).
Mr. Cthoops put a screwdriver in the edge of the backing plate and started tapping it in, moving it around as best he could. He then sprayed the Un-hesive and waited a bit. Then he hammered in the screwdriver under the backing plate in a few different spots, prying it up about 1/4" and sprayed more Un-hesive in there. More prying and hammering followed and it finally broke free.