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I can only agree with your theory on the leakage, this is usually caused by battery leakage and made worse by the black foam that stores it AGM style.
So when you do scrub it down, make sure you rinse the foam thoroughly.
I once had one of the family so badly impregnated that the battery voltage had caused a char in the foam that I didn't spot at first (black on black) it had me searching for the leakage current once reassembled, the thermal cam showed a hot-spot on the foam.
If you come to needing readjustment I have notes on that, actually the photo might already be around EEVBlog.
Oy !
Leak (electrical and chemical....)OK so I spent many hours working on the Metrix MX 52 DMM last night and today.
I disassembled and reassembled it way more times than I can remember, and followed many red herrings, but it's finally feeling much better and now put back together for good.
So in the end ShakalNokturn was right.... the gigantic ghost voltage, which also affected the ohms range, was all due to battery leak polluting the PCB.
I did have corrosion on the negative battery terminal, which also locally / partially dissolved the rubber mat that sits onto the PCB and around the terminals.
I cleaned that with 90° alcohol (didn't have any IPA left somehow, need to order some). Looked OK but didn't fix it.
Cutting a long story short, I was eventually led to decide it might be worth trying to clean it some more.
So since I could not trust my eyes to decide if it was clean or not, I decided to go aggressive and use some "mechanical decontamination" methods instead.
I used a fiber glass pen to abrade the surface of the PCB all around the battery terminals, on both sides of the PCB, then removed the contaminated dust using not alcohol but acetone. Told you I was going aggressive this time...
I also used acetone to rub the back side of the rubber mat where the battery terminals are.
Meter now works much better !

In Vdc, I now get a solid 000.0
In mVdc I also get 0.000 the moment I switch it on, then there is some capacitive coupling I guess, with the noise picked up (?), and the measured value steadily increases, slowly, by about 0.1mV per second. But of course if I short the probes it zeros out just fine. So good enough for me I guess.
In ohms mode it's much better as well. My precision resistors now read either spot on or close enough to it, be it the lowest value of 390 ohms, or the highest one I have, 50K. So a definite improvement there as well.
The "ADP" mode is not good though, it reads 'OL', or a hundreds of counts, instead of zero, when open circuit. It's basically a 500mVdc range. However the mV range itself, the "real" one, is now working fine, so not sure what's going on....
It still reads fine if I apply a voltage though, or if I short the probes, so it's perfectly usable nonetheless.
Rotary switchHad to desolder the RF shields top and bottom to get to it

Luckily the shields were easy to remove, their mounting tabs were soldered only to the surface of the PCB, rather than going through the PCB and be twisted on the other side.
The switch is interesting.... it does not glide over the main board, but rather over a little circular "daughter board" that holds the gold plated tracks. Not sure why they did that... to help with routing the main board ?!

Anyway, switch contacts and tracks looked clean, but I rubbed them with a Q-tip and alcohol anyway, and the Q-tips were black.... so yeah, there again, even if it looks clean and shiny to the eye... doesn't mean it is actually all that clean.... so worth doing.
LCDRemoved / unplugged the daughter board that holds the LCD and CPU.
Pulled the two zebra strips, cleaned them with alcohol, also the matching pads on the PCB.
Found a trimmer at the back of the board, assumed it was there to adjust the contrast. It does. You can access it when the meter is assembled (bar the back cover of course...), thanks to a hole in the main PCB and another matching hole in the bottom shield.
LCD now works just fine. No weak segments anymore, and LCD now has good contrast when viewed from a normal angle.
Display looks beautiful when out of the case... motivated me to restore the plastic window of the top shell, to remove all the scratches that keep you from appreciating how nice the LCD actually is. It's the first time I try to remove scratches from a display window. I thought this meter could be my guinea pig. It didn't go well at all. Tried sanding the scratches by hand with paper. Starting at 120 grit given how big some of the scratches were, then 180, 400, 800, 1000, 1500, 2000, 5000, magic sponge then car polish.
Problem is that you can't manoeuver the sand paper properly, because the window is so small and recessed. So you have to use tiny movements and you are constantly banging against the edges. Clearly I can't do it by hand. But I will redo the job later with a micro polisher with a tiny 1" backing plate, should work much better.
CleaningWell I started with that actually. Took the thing completely apart so I could clean all the bits properly. It's clean now....
CONCLUSIONIt works much better now, but I just don't trust it enough to actually use it....... so I think my Fluke 11 will remain my daily driver for now. I bought it 27 years ago but it's still flawless, super reliable. Unlike the Metrix, it does inspire confidence, and has proved itself for nearly 3 decades now.