Fluke 8845A, for about US$160, from eBay.
A couple of the ranges don't work. I'm thinking that the relays are bad since I hear a thunk when switching from a working range to the broken range.
I ran the firmware upgrade procedure (thank's TiN for the FW download). Unfortunately, I wasn't good at following instructions, and thought the "The next step takes up to 12 minutes. Click Ok when it says done" was a "The next step takes 12 minutes. Click OK to start" message. So, once you click OK, it says to power cycle it..... so I power cycled it as it was sending the inguard FW over the optical link, corrupting its flash. I also now know the commands to directly modify the various calibration constants, so that's nice, too.
Fortunately, the firmware contains the raw data that needs to be loaded to the flash, so I desoldered it, reflashed it, and it worked again. Nicely, I also was able to grab the root passwords for it from the firmware image (different password for the three ports it uses). I _think_ you can also tell it to be an 8846 over the interface and it'll believe you. The 8846 supports USB storage, has a more stable LM399, higher resistance range, lower AC range, capacitance measurement, RTC, and temperature modes.
For me, the USB storage and low-current ranges would be good to have. If it accepts a "MODEL 8446" command, then I'll start purchasing the USB components.