Looking at the power supply section now:
The bad meter happens to have R8 not populated. I'm guessing R8 is switched to 24V/Vout when you move the dial to the 'V/mV' range to drop the supply output voltage to ~12V.
Since you only need 10V max output/input perhaps this saves power or reduces power dissipation. Something getting 24V when it expected 10V could have caused an issue.
I'll try populating R8 but I'm thinking the damage is already done.
Also note the use of a 25V cap on 24V supply
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edit: R8 drops the boost supply output to 10V when it is in DMM mode or the dial is between indents. All process ranges sit at 24V, so those shouldn't be affected.
edit2: U5 is the 2.5V reference, pinout matches LM236 or LM136-2.5, 20ppm. Its marked '10091', so maybe from a custom order?