okay, had my hopes up that I found the issue when I saw some solder-like material between the guard and input traces on U4, but seem to have been nothing. =/
Anyway, the info you asked for.
Input Impedance:
DC mV: 9.9845M
4VDC: -1.45M-1.74M (all over the place)
40VDC: 6.6M (all over the place as well)
400VDC: 9.990M (rock solid) (87 even sees 1.0V coming from my 189's resistance measurement)
1000V: 9.980M (ditto).
So the issue would seem to be the 4VDC and 40VDC. Hmmm...
Measurements of 12V DC PSU... set it to 1mA so I didn't risk blowing out my wimpy 1/4W input resistors I hacked in there). PSU always read 0mA. Actual measured draw on each range is listed in parenthesis below.
4VDC = OL (1.275uA)
40VDC = -25.55V (all over the place) (1.223uA)
400VDC = 12.0 (1.195uA)
1000VDC = 12 (1.196uA)
Calculating from that, the input impedance for each range, 12VDC input, with the listed currents, would be 9.411M, 9.811M, 10.042M, and 10.033M, respectively.
The 40VDC range is interesting since with no input, the 87 reads -33.45VDC. One would think with 12V input, it should read -21.45VDC. Huh.
R58 and R59, however, both check out as far as resistance. There's a 1.58V drop across R58, and a 0V drop across R59 (which, I'm not sure I understand, but like you, I have a difficult time with schematics... especially since Fluke didn't actually label the parts on their schematics) in DCV mode. Reading through the service manual section on Voltage measurements... I'm either thinking U4 is bad, or they've way oversimplified things... Because somehow, Q1, Q2, Q6, Q13, and Q14 enter into the equation.
One thing that keeps me wondering... did you ever manage to measure C20 (capacitance, maybe ECR/Resistance as well if you can)? I do see a bit of voltage on it in DCV mode...
Alright, time for bed.