Step 1 is to totally ignore the supported versions listed in the release notes. They're full of lies and claim that my laptop (an R50p with an Intel 2915ABG wifi card) is supported when the installer thinks otherwise (except when they claim my laptop is unsupported and then install anyway). Fortunately Lenovo are nicer than most and provide download links for older versions, and so after trying multiple ones I eventually ended up with:
Access Connections v6.26.79
Hotkey Features Integration v3.81.0100 (later versions refuse to install)
Power Manager v6.68 (but see below...)
Protip: binary search is the way to do this, as O(log n) is much faster than O(n).
That combination all installed and seemed to mostly behave - importantly, I could now enable the wifi radio again! However that's not the end of the story, because now that I had the power management tools installed I fired that up to put together a better power scheme than the default, and in the process apparently crashed the embedded controller. And wouldn't you know, but the embedded controller is responsible for such things as making the keyboard work. And the mouse. And the display. And, most annoyingly, the power button. The only way to reset it is to remove the battery.
Some searching threw up a known bug where the embedded controller hangs if queried for detailed battery status - I suspect that the power management tools triggered this, as I'm using a significantly newer and shinier version than what was available when I was running XP on the laptop. So, next task is to try older versions of that until I find one that no longer triggers the crash.
On the hardware side of things, the improved heatsink turned up and is waiting to be installed. However the processor upgrade did not appear - the online tracking shows that it never made it from China to Europe and the random eBay seller was not particularly helpful when I initially prodded them over it. I can't be bothered to dispute the transaction for all of £10, so I'll probably try again with a hopefully slightly-less-shady eBay seller.