Hello again and thanks in advance,
Even though the boards are identical, mine has a real ATmega 328P, instead of that U1 chip on the picture I linked to. I didn't catch the difference until after indman pointed it out.
Also, I removed U7 and it's still showing Zener. I have removed before, out of desperation more than anything, L1, the R6 and R7 voltage divider, U6, D1, R16, D2, basically anything less than 2 traces away from the KAA probes. In all cases, it shows the Zener test and a random 3.4ish voltage.
I forgot to mention, whenever I short all the 123 probes, the tester goes into selftest mode no problem, so there might be some hope left for the device.
I wouldn't mind losing the Zener functionality as long as the rest of the tester works, as I mostly use it for MOSFETs and the like.