Well what I ended up doing was to grind down the entire flat on each side, but angling back slightly to the spine, like a dagger grind. That dropped maybe 1/8" or so of thickness at the spine. Then I added a long swedge at a steeper angle. I am trying to find where I put my kitchen scale to figure out how much actual metal was removed.
I got mixed results. On the one hand, while I only moved the balance point back about 3/16" of an inch - which isn't surprising since so little weight is in the handle, comparative to the blade - the blade is noticably easier to move in figure-eights. It is now closer to my modded 1311.
On the other hand I should not have tried to grind after it bit my right thumb, because that cost me control on the grinder and . . . mistakes were made. Especially since I was using a fresh 36 grit belt. It will take a lot longer to clean this up than it did to just hog off steel, sigh.