Well, it's done. After a week of trying this and that, I finally got DSL (DamnSmallLinux) rolling on the Fujitsu B2131 last night.
To remind folks what the challenge was (and is for some of the linux dev teams out their who claim to support older platforms): Install a fully-functioning OS on a laptop machine built in 1999/2000 without a CD drive.
DSL has a great boot floppy image that works with their embedded version of the OS installed on a Flash drive - ok, the flash drive made the challenge less problematic than originally described.
However, I lay the challenge out to all of the Linux distros: Create an across the INTERNET (not that crazy PXE boot stuff) install that can be started with boot floppies.
The B2131 has a large enough hard drive and enough power to run Xubuntu, but installing it easily (i.e. my 10 year-old son could do it) makes modern linux distros completely unreachable for people trying to easily make old machines go.
So, linux geeks, think you can do this?