This is the part where I eat my own words. I didn’t think it possible, but it works. The Geode is an i586, and logic says that a system tuned to the 686 — which regularly resisted all efforts to run or even boot on K6-series machines for me — seems quite happy to plunk along on my XO-1. See for yourself.
The method was identical to the Crux version I had been using for a few weeks — basically importing the OLPC kernel, modules, firmware, etc., straight into the Arch installation. It still seems a bit barbaric to me, and as an Arch fan it’s less than satisfactory since it undercuts a lot of what Arch is about. But it works.
I stuck with the same GTK1.2-ish setup I had with Crux (Dillo, XMMS, Xfe, xterm and the like), and performance is about the same.
I still want to get a proper, pure, non-OLPC-reliant system into place, but this is satisfactory for now. I get all the frills and benefits of Arch without having to recompile every little fragment of software that is implied. That gets a little old on a 430Mhz system. 
That looks like windows!