Well, I found a solution almost as soon as I posted my question. The answer is this: the Matchmaker simply won't work with the AXS controller. I don't know how on earth that simple ergonomic design got overlooked. It was the first thing I noticed when I installed the controller. My thumb had no room and was hitting it. I even moved my entire brake lever/controller assembly over about 1/4", which was totally counterproductive given that my levers were right where I wanted them to be, but even that adjustment didn't work.
So I moved my lever clamp back to where it was, ditched the Matchmaker, and used the standalone handlebar mount on the stem-side of my brake lever. FINALLY. This is actually comfortable and workable. Now I'm ready to give the system a try.
Here is the original setup.
Then after I ditched the Matchmaker and went for the standalone clamp. Much better and clearance for my thumb.