Please see the schematics, p. 9-10 of service manual:
On 10M and 100M Ohm ranges, which both (?) fail, a constant current of 17.5µA is created by R201, 400k.
(I assume, you measured 240k on the 10MOhm range? But 180k correctly on the 1M range?)
All other, lower Ohm ranges, including 1MOhm, use R202, 40k for 175µA.
This 17.5µA current creates a 0.5V voltage drop over the 28.57k resistor in hybrid U102-D.
OpAmp U201-B regulates the output constant current , so that the same voltage drop of 0.5V over the 1M reference resistor in U102-D is generated.
That means, 500nA have to flow from the floating supply Ufl. ~ 13V over 1M to FET Q202
The floating supply Ufl. should be checked in lower Ohm ranges, as the foregoing problems were caused by a defect CR203-A, as far as I remember.
I bet, this is OK, as all other lower ranges are working correctly.
R201 may be defect, and may measure around 300kOhm.
That you can perhaps check
in situ with another DMM, but with de-energized 34401.
There's also service note 34401A-12, indicating a serial problem with this resistor:
http://literature.cdn.keysight.com/litweb/pdf/34401A-12.pdfMaybe you don't find such an extreme drift... because normally, due to their technology, TF resistors always drift towards higher resistance values.. then U101-D might be fishy.
Or first check R201, top and solder side for any dirt, which may create a parallel parasitic resistance.
Frank