Knowing no end of Multimeter repair, I decided to pick up a Keithley 196 I found via eBay, then managed to purchase it privately through PayPal for a song (~$50).
The unit arrived a bit worse for wear, but with some Superglue and JB-Weld, I was pretty much able to repair all the case damage. The power switch also needed some percussive maintenance to get it to work reliably. Visual inspection showed only that one of the two Polystyrene Capacitors (68pf 500V) had been melted at some point. After poking it with a probe, the cap started making a very bad buzzing noise, so I replaced it temporarily with a Silver Mica cap of the same rating.