I spent the morning working on the Linux build in my Ubuntu distribution, and it works. Horray for BlitzMax - half a day, 3 issues total, and it ran.
There are definitely still problems - I didn't have time before to see more than that the game was running, but some of the fonts were off and there were some nasty graphics artifacts - parts of the desktop were flickering in an out through the game.
I'll see what I can do to resolve that stuff, and if I can get it working before next Friday, then that release will be our first with a Linux build.