I was wrong about the model number being derived from the serial number, in the manual, under SCPI errors, there is this:
+821,"Controller and measurement board model numbers do not match"
+822,"Controller and measurement board serial numbers do not match"
So both the model and serial number are stored separately in two places. The controller here is referring to the front panel - so swapping displays will cause the multimeter to error.
Interestingly, there is also this error:
+820,"Model and serial numbers not restored"
So I think it is safe to assume that the model numbers are stored in at least three places across the two boards (likely twice on each board).
The main processor (the spear320) has a 32 kB boot-rom and an 8 kB sram. So I think it is unlikely the serial & model number are stored in there. The processor has a flash and ram chip above and below it. The serial/model might be stored in there but I'm guessing that it isn't - it makes more sense for that just to hold the windows ce image, as then a firmware update can't make the multimeter forget its identity.
The front panel has an NXP LPC932 - an 80C51 microcontroller with 8 kB flash, 768 bytes rom and 512 bytes eeprom. If I was designing this, I would have placed the serial and model in that eeprom (their are no other external memories on the front panel), as you could update the microcontroller's firmware without the eeprom data being lost.
With the measurement board, I think it is unlikely they would store the serial & model in the FPGA as it hinders firmware updates. There is the TI cortex-m3 on the bottom of the board, but for the same reasons as above, I think it is unlikely they would store them in there. So the question then is, where do they store serial/model and also where do they store the calibration constants? My guess is U904 in this image
https://www.flickr.com/photos/eevblog/16171847343/ - it looks like the right size package for an I2C eeprom, and it has pins 2 & 3 tied together (suggesting they might be address pins). Unfortunately I can't find any details on it.