I’ve built multiple spokeshaves of that type (using the kit from Ron Hock, which is now sold by LV), and I’ve found that after the initial adjustment, the only time I fiddle with the blade is when it needs sharpening. I now bore the screw holes oversize and adjust the cut mostly by tipping the angle of the spokeshave, but if a small adjustment is needed to the blade, I bought some very thin brass washers and pop one of those under the blade to increase the gap, or take a chisel to the wood where the blade mounts to decrease the gap a little.
I also generally set up the blade so it cuts slightly thicker on one side than the other, so if I’m cut to on the right, it’s a deeper cut, and on the left, shallower.