I finally got around to start the thinning project last week. I was using p220 grit wetordry sandpaper I had. I used it wet on a pretty flat and lacquered piece of 1"x6" (having it wet was the only to keep it from sliding around). It was pretty slow in my opinion, spent maybe 30-40 minutes, used up probably 40-50% of the paper, thinning a good 3cm up the side of the blade. It still looks like a long way to go.
Is there any problem to use the rubber kitchen cabinet lining as backing for the paper, and dry? I'm okay with the convexing, but will any problems arise from thinning too extensively with soft backing? For me, that is the most efficient way to keep it from sliding around, and the ability to use dry paper.
I went to the automotive parts store, of the wetordry paper, the coarsest they have is the 200. They have non-wet coarser paper, may get that if it's okay to use dry with the rubber lining.
BTW, thanks for all the replies!