LIGHTWEIGHT LINUX DISTRO NON PAE INSTALL
Theoretically, the ALIX boards support PXE installations, but I just used QEMU ( qemu-system-i386) with a 4G virtual drive, booted the basic 32-bit Slackware install disc 1 from virtual CD-ROM, used slackpkg to patch the OS, install various additional packages.
Installation is the same as for any semi-embedded platform. It's patchable and has good ALIX support. Fortunately from my testing today, Slackware 14.2 (32-bit) works fine on my ALIX 2d13 board. You're right that non-PAE i586 options are dwindling in the Linux family. Since this is now a "famous question" and I did some further digging: Alpine Linux supports non-PAE processors and runs perfectly fine on my ALIX.1D.
LIGHTWEIGHT LINUX DISTRO NON PAE UPDATE
This will require some tedious work to get everyting up and running, but who am I to complain ) Update ()