End of the Walker
I finally found a way to get Final Fantasy 14 working again thanks to a GitHub gist. The author essentially replaces the Final Fantasy 14 Protonfixes launcher script with one that installs FFXIVLauncher into the same Wine instance Steam uses to invoke the game itself. It then uses this launcher instead of the broken one Square-Enix demands. Since Steam invokes the script within Proton, the replacement launcher passes the expected steam account ID to Square and everything magically works.