Late to the party... as usual...
One of our brothers over on your side of the pond...
@Grimly maybe??? recently pointed out that there's a handy pry point on the sump plate. Right side aft. Next time I pull one that's stubborn, I'll give that a go.
For a flat surface to work the plate on, my table saw has a nice flat, machined cast iron top... prefect for surfacing... so there's another option. Any saw with a cast iron top will be machined flat and do the job.
I use contact cement (3M Super 77) and glue the paper down. That way I can butt multiple sheets together to make a large work area for stuff like the side covers.
Another thing I'm doing now is starting with 240 wet/or/dry paper. It saves a lot of elbow grease. 240, 320, 400 and done.
I also use WD-40 for a lubricant. Seems to work better than water for keeping the paper clean... and not rusting the cast iron top.
...and yeah... dragging a single edged razor works great.