I'm having a problem where the N900 says 'battery empty' and shuts
down, then, after I wait a moment and start the phone back up, the
battery still has around 40% charge left (as determined by "lshal |
grep perc", which may be a Klingon command).

The batteries I'm using are oldish, but I doubt that alone is the problem.

This routinely happens when I'm browsing online - talk about annoying - though that may be a coincidence.

This is definitely behaviour/proof of old used battery.
Just get a new one.

As peterleinchen says. That it happens whilst actively using the phone is definitely not a coincidence. The battery's internal resistance increases as it ages. The voltage on the battery's terminals equals the internal voltage minus the voltage drop. And the voltage drop equals the current drain times the internal resistance. So it should come as no surprise that the extra load while actively using the device should cause enough viltage drop to cause problems. I once had a phone that lasted 7 days on standby but would reboot when I received a call with the battery 90% full. A new battery was the solution. Get a new one.

I suspect you're right.

Ideally, rather than suddenly collapsing and turning off, the OS
should detect this situation, then throttle-down or pause some
processes, and give the user a warning; then, you could close some windows, lower the screen brightness, etc., and continue, without ever having to shut down. The batteries are older (they only charge to 95 and 84 percent), but they're still quite usable.

In theory, yes. And it does, when the battery voltage decreases gradually. The full charge is about 4.3V, empty about 3.2V. When the voltage gets to 3.5V, the OS starts crying for help. The exact numbers may differ slightly but you get the picture.

Unfortunately, with old batteries, you can easily have something like 4.2V which looks like an almost fully charged battery. But add some load, such as receive a call, and the voltage drops unexpectedly below 3V, or even below 2V. This is not only below the "empty" threshold, it is way below the lowest operating voltage of the CPU. To all intents and purposes, it looks to the CPU as if the battery has been pulled out. There is nothing it can do.