I have looked through the whole signal path, sorted out details and re-done measurements.
Now the absolute reading I get for R1=120R is
0.213uVrms which by rule of thumb, multiplied by a factor 6 is the ptp value, in this case
1.28uVptp for the plain vanilla LTZ1000ACH circuit.
I also checked a few other current settings, R1 values, and the ratios in the diagram I posted the other day are repeatable. For example, with 249R for R1, I get 0.28uVrms noise. With the ratio from the other day, 1.33 for 249 ohm, times today's 0.213uVrms = 0.283uVrms.
The most important change from the other day was to get rid of the AC coupling for the ADC, replacing the cap with an external 50x larger value (2.2uF instead of the internal 0.047uF) which with an input impedance of 1Mohm gives a -3dB HP at 0.07Hz.
The second thing was that I changed the sample rate down to 32Hz. The instrument manual said the minimum is 1000Hz (set by a DDS) but when I query the instrument, it replies that the valid sample rate range is down to 32Hz. As it's a delta-sigma converter, now that I sample at 32Hz, the mains frequency is gone, no need for analogue LP filtering. I sill added 0.1-10Hz brick-wall filtering. Without it, the noise was about 25% higher, as expected.
Now to the strange and hopefully very positive part. Setting R2 to 5.6Mohm, did
NOT increase the noise! As far as I can see.
I have checked everything I can. The instrument noise is more than 2 orders of magnitude lower than the measured value. The OP noise should be a factor 6 lower than the measured value (0.2uVptp 0.1-10Hz). The signal "looks" OK, no clipping or abnormal offset. The voltage from the circuit is the same as the other day, 6.999xxx V with the 5.6M setting, currents look OK etc.
Can someone confirm this experimentally? Is there a theoretical explanation? Could the noise cancel? Or did I simply make some lousy mistake?
The best would be if someone could confirm / reject this experimentally. IE: throw in a 5.6M resistor for R2 instead of the nominal 68K. And measure noise for both R2 values.
Of course, the problem of getting ultra stable resistors at 5+ meg remains.