Are we geeks or aren't we? If linux runs on embedded devices like watches, then it should DEFINITELY not be that hard of a challenge to run it on the laptop of the TS.
I suggest building a small LFS distro and just adding a console text editor like vim. Then rm all of gcc.
XFree won't work I think, it will be swapping like hell.
But isn't the power of linux the console? Learn LaTeX and type in vim. Or maybe check out an svgalib text editor? I know links2 works great in svgalib, I'm guessing a text editor shouldn't be a big problem too.
The only problem will be to stick a linux kernel in 1 mb of ram. Try skipping the most of the kernel and only retaining the essentials: console, disk+filesystem and svgalib support. Skip everything else (who needs an RTC timer anywhay, buy a watch ).
In any case, it will certainly boot faster than Windows 3.1