I managed to pick up 3 "broken" Keithley 2000's for $600 including shipping to Australia. So far two have arrived, and one of them repeatably passes self tests and spits out some believable looking numbers. The other is a bit more interesting: it fails self tests initially but after running for 10-20 minutes it passes everything. When it first starts up there's also a lot of noise on all ranges, so I assumed there was a problem close to the ADC.
I first checked the voltages and found +15 and -15 to be +15.9 and -16.0, so I assumed this was the problem. I checked the other meter and found the voltages there were also high, so I assume this must be common and not an issue.
I had a poke around with some freezer spray and a heat gun and found TF-245 pins 3 and 14 are open circuit when they're supposed to be 15K. After the chip warms up the resistance drops to around 10K which also isn't exactly great.
I've since found the TF-245 is notorious for failing, but doesn't seem to be easily available. I've contacted Keithley to see if they have the part available, but if I'm not able to get it from them are there any replacements? I could probably cram the resistors on a small PCB with castellated edges, but I doubt I'd be able to find the exact values the chip has.