I was going to mill the height down to match the WEPS clamp and tap one of the undersides, just like the WEPS clamp, and put tape on the jaws so the hardened steel clamps that I have dont mess up the blades.
I have following idea. Flexing is far more severe when you are doing rubbing motion to raise a burr. When you sweeping, you should use very little pressure, so there is much less flexing. Flexing somehow changes the sharpening angle, so you are raising the burr and sweeping under different angles, thus maybe not hitting the edge when sweeping.
I suggest to set particular angle, raise the burr through rubbing, then raise the angle somehow (maybe 2 degrees will be appropriate) and then continue with sweeping with light pressure. Drawback is that you increase minimal available sweeping angle, and I have sujihiki made by japanese carbon steel, so this steel can handle quite acute angles.