Interesting thread. I was actually wondering about something similar. I can get two Force eTap shifters for cheap (cough, 380 bucks), but I currently have a full Apex 1 set with Apex brakes. They're fine and I recently replaced the pads, so why bin them? I asked SRAM whether I can fit Force Etap shifters and make the brakes work, and they said it will physically connect, but it won't function properly and safely. This is what they said about it:
No, unfortunately that is not possible. Physically you can connect the Apex callipers to the AXS shifters although you have to shorten the pipe a lot because the connection on the shifter is different.
However, the ratio between pistons in brake lever and calliper is different with the Apex brakes than with the AXS brakes, so the brake is not reliable, so do not be dangerous !!!
But when I read the posts from some people with experience here I'm like wtf is this nonsense? What's smart? I either buy 2 shifters for 380 bucks, or buy 2 new shifters including callipers for 580 bucks. It's a 200 euro difference, but obviously safety and reliability is important here.
edit: SRAM USA also answered my mail and told me it's unsafe to do because of an other leverage ratio.