I've been thinking seriously about tearing it open, and replacing
whatever simple fixed-resistor slow-charge circuit it has with a
proper faster-charge-and-real-cutoff circuit of some sort. I'd have
to replace the wall wart, most likely, to get a decent charging
current.

The simple, no-cost solution (which works for me) is to use the Dust Buster
until it runs down, then charge it overnight and take it off the charger.