Very disappointing news: the fix that I had hoped would solve the problems with the Linux version did not, in fact, do so. I am still looking for alternative solutions, but I cannot offer any sort of timeline. At the moment I am stumped.
I would encourage anyone wanting to play the game on Linux to consider purchasing the game at https://mikegentry5.itch.io/anchorhead instead. It is the exact same build as the version that was to be offered on Steam, except that it works.