Just connected two 1 GOhm resistors. In 2W mode and with 100 PLC the variation is 853,4 to 853,8 for one resistor and 884,7 to 885,1 for the other one. Spread/walk is independent of guard connection and this was using short unshielded cables. Addition of a 2 nF high voltage cap reduced short term noise but not the spread. Anyway the instrument should calibrate to 1 MOhm or better.
Spec seems to be +/- 5 MOhm, so our R6581T wouldn't have that problem. Also i think the remark of Mickle T. may be correct, yet i haven't seen a demonstration that a R6581 is any different/better for the DC part.
Regards, Dieter