A couple things have helped. First, I’ve stopped using the knurled adjusters on the 151. They are too coarse. Instead, I am advancing the blade with them on a piece of scrap until the blade isn’t quite cutting. From there, I tap with a hammer to set the depth of cut. This is giving me far more control and is allowing a finer shaving. Second, I’m tightening down the blade significantly more than before. To some extent, I use the hammer to advance the blade and the knurled knobs to bring it back if I go too far, then relax the knurled knobs (take advantage of the backlash) so that tapping with the hammer will work.
I also have a #52 and I think it works better than the 151. I can tap with a hammer, as just described, but I can also tighten and loosen the thumbscew which gives very fine control of the depth, although over a limited range.
The problem isn’t entirely gone, but these things have helped. I’ve also played with putting a camber across the blade for working on wide stock, and I think that may help a bit. Not sure yet.