Some encouraging progress. I have had no luck testing with shims, but today I tried far, far more shimming than I thought should be necessary near the mouth. This is 3 layers of blue tape on the mouth plus another half-strip to account for some possible twist. That should be in the ballpark of 0.011-0.015 of shimming. The improvement in iron grip is substantial and probably sufficient for use. It also works with thicker shimming. You still have to set the wedge pretty firmly but it holds better than anything else so far. Now I know for a fact that I don't have a hump this big anywhere on any of these mating surfaces, or a wedge angle off by that much, but it makes a huge difference.
I think maybe I have been thinking about all this wrong. I was thinking if I made perfect, clean surfaces that fit together very closely and had subtle high spots (a few thou) in favorable areas, it ought to work. I was rejecting the possibility that the high spots might need to be much larger than that.
That strategy had worked OK for the few bench-type planes I've made, but in this case we have a very small and delicate wedge and a thinner, less rigid blade (the tang is only ~0.200" x ~0.100" cross section and will be unhardened) and far less contact area overall, plus a significant distance from the wedge tip to cutting edge, and then wedge tip to abutment/breast. In addition to that you have significant lateral forces from the way the plane is used. I think this is a totally different ball game.
I think what you actually want here is to aim for elastic deformation of the wedge and/or blade in order to develop the spring force necessary to hold the iron in place laterally. I'm not a mechanical engineer, but I remember that for a simple spring the force of the spring is proportional to the displacement. And I know that the force of static friction is proportional to the normal force (which in this case is coming from the wedge action and the spring action.) More deformation (displacement), more static friction than you could get from the wedge alone. The tip of the wedge may be bendy and delicate, but once you preload it it can exert a lot more force!
I am staring at some pictures of metal rabbet planes and wondering how it took me this long to realize the high spot near the mouth might need to be exaggerated. If you look at this photo of a Stanley #39 (not mine) that has a fully-hardened machined steel blade and a cast iron body and a metal wedge, a much wider blade and a much wider wedge, you can see they put a land that appears to be at about 1/32" thick near the cutting edge. I measured my Millers Falls rabbet plane and it also has a land of about 1/32". Compare this to a metal bench plane whose frog is machined or lapped flat. You might argue that this helps them cut the cost of machining the entire bed or producing truly flat blades but I'm not totally convinced. Even the Veritas jack rabbet plane and skew rabbet planes have this feature, as do metal shoulder planes. Block planes have this feature too. I think it shows up on a lot of planes that don't have the luxury of a huge bed/blade contact area. The cap irons also have significant reliefs.
The other thing I am realizing is it is probably not a fair test to try to move the iron left, then right, then left, then right, etc. as that is not a pattern of force it would encounter in real use. Most likely the wedge will eventually loosen if you wiggle the blade laterally enough no matter how tight it is. (No matter how you adjust a plane you always have to tap the wedge, after all.) If you can't move it in one direction immediately after setting the wedge that should be sufficient.