I am the OP, replying with the solution I found.
The symptoms were very much as if a small resistance had been inserted in series with the left speaker. Peering at the circuit board, I noticed a pair of large-ish electrolytic capacitors near the connector that carries the speaker outputs, a common feature to remove the DC offset when driving speakers from a single-rail circuit. I also noticed that the cans were a little swollen. I guessed that the caps drying out or going bad could increase their effective series resistance, which could explain my symptom.
I opened up the case and replaced both caps with new low-loss audio-quality 1000uF 16v electrolytics (same ratings as the parts I was replacing). It worked! The stereo balance is now perfect.
I’d never heard of bad caps messing with the power of audio output circuits, only of them shorting out power supplies. But it seems like this is a real, if less dramatic, instance of the bad caps blight.