Can I remove my thru axle when the lever is disengaged?
Because necessity is the mother of solving problems caused by poorly designed components, I'm answering my own question.
I tried vice grips, as someone recommended, but the alloy in the axle was too soft to get any bite before they slipped off (did manage to mangle the exposed threads though, so that was fun to file off before removing it).
The solution that ended up working was to jam (force) a ball-end hex wrench that was just too big into the open end of the axle, press hard, and turn. For this axle it was a 3/16&quot; (4mm was too small, 5mm was too big). As soon as I got it backed off just a hair the lever engaged as it should, and all was right with the world.
For reference, I also tried this approach using various sizes of Philip's head screwdriver without success. My next plan was to file a slot in the threaded end for my jumbo sized flat head screwdriver. If that didn't work, I was going to buy a reverse-treaded screw extractor. Based on my experience, either of those approaches should have worked as well.
I'm fairly confident that if I had taken this approach from the start I could have salvage the axle (at least until my new one comes in the mail). Live and learn.