I've done a bit of thinning... A few years back, I found a very inexpensive chef's knife with what appeared to be very good steel. I thinned the blade to about 0.010-0.015" thick at the shoulders. The results, in terms of performance, were impressive, so I bought about twenty of them (at the time they were less than $15 each) and thinned each of them to give as Christmas gifts to each of the women in my circle of friends and family. I'm a serious knife sharpener, so each recipient was given instructions on care along with lifetime free sharpening. Several reported that it was by far the best kitchen knife they'd ever used. Most never came back for the free sharpening, so I assume they were used and abused.
The thinning was done on my 6X48 belt sander in the horizontal mode, with my finger tips applying pressure just behind the cutting edge. If I sensed any increase in temperature, I immediately went to a water bath to cool the edge. The key was to start at a coarse grit - about 180 grit and proceed up to 400 grit in steps of 220, 320 and 400, turning the angle with each grit change to watch for scratch removal. Trying to take off too much steel with a fine grit produces too much heat.
Thinning with a stone seems to me to be an exercise in boredom. High-end Japanese knives sharpened on whetstones takes hours and hours and hours - and that's just for sharpening. Thinning might take days. I think you might get a better return for your time by stoning for a wide (large radius) convex at a high polish. This produces an edge performance approximating thin shoulders.