So basically if 3v is noisier than 30v range, there is a chance that the precharge amp section of the hybrid is dead?
That actually seems less likely, but I suppose it is possible that a switch is leaking there or something.
Looking and your videos and your reported results seems a bit confusing. If you have a display bouncing from 11 to 13 counts, I would call that 2 counts of noise and 12 counts of offset. It's important to maintain the distinction. Perhaps you could make a chart of the offset and noise in each range with AZ on and off. So, after a set warmup--say an hour--go through the ranges from 30mVDC to 300VDC, a set time--say 15 seconds--in each range and write down your estimate of the min/max variation (noise) and average (offset). After you do all the ranges, go back with AZ off and do it again. I think this would really help me fully understand what you are seeing.
As far as what is normal and what is not, on my presumably working model AZ makes very little actual difference in noise, but it does appear to move faster because you see twice as many readings. Letting it sit for few hours in the 3V range with AZ off resulted in 1 count of drift in that time. If you have noise, say in U101, then AZ won't really help and may make it worse because each AZ reading will be affected by the noise differently--so your zero will be changing constantly. At least with it off, the CPU is using the same value for zero all the time. Short term, that could actually be more stable if the noise is high frequency--less than an A/D cycle-- and random.
Normal offset on mine is a few microvolts--about 4.0 when first turned on, then +1.0 to +2.0 (10 to 20 counts) on the 30mVDC range when warmed up. All the higher ranges are 0 or 1 counts. Causes of a steady offset could be actual voltage on the inputs at any point prior to the junction of the input amp U101 and the AZ section (which I believe is S8DC inside U102) or an fixed offset error in the AZ circuit. All of that would be inside U102 and probably would be an issue with the analog switches. AZ should really take care of any other offsets anywhere else along the chain. Of course there will be a residual offset and that is taken care of as a calibration constant, provided that it is stable.
You've probably read the manual pages 7-A-1 through 7-A-4, but they're worth studying closely. Some of the tests, such as the part where you supply a precision 3 volts, short pins 2 & 6 of U101 and then make measurements with a precision voltmenter, probably require better equipment than you have. You may have also seen the short part where they essentially tell you that if you have noisy readings in some ranges, replace U101 and if that doesn't fix it, U102. Obviously nowadays that is easier said than done. Try to make up that chart and I'll think a bit more about how you might be absolutely sure what the issue is. U101 may be findable, U102 not so much....