@3dreamer
I ended up getting my problems all sorted out. But I had to do several things:
Increase the supports for my bed so that it was closer to level to start with. My bed is a bit over 600 mm x 600 mm and wasn't sufficiently supported, so there was a significant sag in the middle. Now I still have some sag, but my maximum variance across the surface is 0.387 mm.
Fix the twist in my gantry. There was a couple degree twist along my y-axis, and due to the location of my BL Touch relative to my nozzle, just a degree resulted in a very significant height error. One degree of twist was over 0.4 mm of height error.
I picked a common point on one corner for my z-axis datum, my probe z offset, my bed tilt probing points, and my bed mesh compensation.
Performed a high resolution map (21 x 21) at temperature.
Modified my macros so that for every print it will do the following:
o Verify that the axes have been homed. If not, home them.
o Verify that the bed has been adjusted for tilt. If not, adjust it, and home z again.
o Turn on bed mesh compensation.
I do not like the commonly accepted approach of using the center of the bed for my z datum. I work in a field where I'm very conscious of how things fail, and I don't want my datum at what is most likely the lowest point on my bed. If, for some reason, I don't turn on bed mesh compensation and I'm zeroed at that point, them I'm likely to run into my bed as I move away from the center and screw up my print head and PEI sheet. So I want my datum at one of the highest points.
Also, I want the corners of my bed tilt and bed mesh to be identical to my datum point, and use the same exact point for measuring the probe's z offset. In this way, it's easy for me to verify that everything is working right. My bed mesh should show zero compensation at that corner, and because I've already corrected the tilt, all four corners of the bed mesh should show almost zero compensation.
It's been a few weeks and several km of filament since I last took a bed mesh map, and my prints are rock-solid every time, now.