Finally, I've upgraded this site to WordPress 1.5 "Strayhorn". Not as straightforward as I initially thought, as there were too many custom hacks from my previous install. I've also changed the theme slightly to get rid of the sidebar completely, replacing with a navigation bar at the top.
None of my plugins is working yet, and I can imagine that many places are still broken. I am too physically ill to get the upgrade done in one go, so I guess I'll gradually patch it up throughout the week.