The square wave curve dues show quite some undershoot. However the ringing is not resolved to the low horizontal resolution. However there seem to be no overshoot - so it could be a problem on limiting, not just the (linear) compensation, which would be symmetric.
The picture ADIN(Y)_PIN20(R)_AZON_BACK-3.jpg also shows clear undershoot. The odd thing is the gate voltage is still going up smooth, so the filtering with C026 seems to be enough. A strong overshoot, that is not filtered out by C026 might be a problem, as it could cause leakage to the gate. So far it looks like there is sometimes quite some overshoot, but C026 is still good enough to filter that out.
However things might be worse when doing current or resistance measurements: here there is not extra delay from C026 and thus trouble is expected with significant overshoot - this could for example be the cause of the trouble with the 1 M resistor measured in different ranges. So preferable there should be less ringing with the amplifier.
The odd thing is the ADIN_Back-3 curve showed today looks completely different (much better) to the tests before, when looking at pin 10 instead of pin 20. Looks like this curve is with a larger C026 and thus the FET turning on very slow so that there is less undershoot and less overshoot too.
The input current is highly voltage dependent. So it does not make much sense to show an effective resistance. I would take something like the slope of the discharge curve over a much smaller range (e.g. 2 readings) and give the current values for a few voltages to look at, like -8 V , - 5 V and - 3 V.
Again - R83 much larger than 10 K would not work as it would not allow to turn off at -12 V anymore. So if it needs to be a bit slower it would be about increasing C26. 1 nF is likely too large, but may be OK for a test. This test clearly showed that the is a kind of timing problem with the switching, as slower switching is causing less input current. However making C26 larger might solve the possible trouble on the "back slope", it could cause trouble at the front slope in that Pin 20 is turning off fast enough. So my guess would go towards a slightly larger c26 and slightly smaller R083 (e.g. 220 pF and 3.3 K). Thus the input channel would turn on a little slower due to C26 and turn off a little faster due to smaller C26*R083. In addition one might have to add a way to speed up the downward direction when the guard voltage is dropping fast. This could be something like 5 K and a diode ( kathode towards guard) in series between the guard (=pin28) and pin 20.
The test with the 1 nF cap seems to indicate that the problem is more with the back slope and not with the front slope.
However having 1 K for R083 also looks like a small improvement.
So there might be problems at both ends and also the overshoot problem is still possible with the original 100 pF in place.
I guess it would be a good idea to check a simulation of the input stage to get an idea of what performance to expect and where possible fixes for overshoot could be. For me that amplifier is a bit to complicated to do that on paper. relying on the compensation of the OP07 could be a problem though as it would requite a good model for that OP.
Edit:
I did a short simulation, but I still miss a suitable model for the U401. With 2N3819 used as JFETs, the circuit kind of works, but it shows a tendency to not so well behave when recovering from large steps. This would kind of supports the observed large overshoot after negative saturation and better behavior when in the linear range.