I have come across something that looks interesting. Looking at the 1071 service manual the circuit around the references is a bit more involved. There are more steps in the resister divider network that is used to set the value of the reference voltage. The boards are the same but the resistors R41 - R45 and R88 - R92 are all fitted to the 1071, whist only R42 - R43 and R89 - R90 are fitted on the 1065, 1061, and 1061A. Both the service manuals describe the step to set the reference voltage, however the voltage is set to a order of magnitude better on the 1071.
The values on the 1071 are R41=169R 1% 10ppm , R42=84R5 1% 15ppm , R43=42R2 1% 50ppm , R44=21R0 1% 50ppm , R45=10R5 1% 50ppm , R88=169R 1% 10ppm , R89=84R5 1% 15ppm , R90=42R2 1% 50ppm , R91=21R0 1% 50ppm , R92=10R5 1% 50ppm
On the 1061 et all:- R42=196R 1% 15ppm, R43=97R6 1% 50ppm, R89=196R 1% 15ppm, R90=97R6 1% 50ppm
EDIT.
I ment to say i have no idea what, if any, of the concequences of modifying the reference selection part of the circuit to the 1071 specs would do to a lesser model, so dont try if your not confident in recalibrating your meter. I posted this for information only