I'm a bit surprised and glad to find this topic. I am troubleshooting my HP3478A input hybrid also. The fault that I am getting is that when I turn it on, then everything works fine. All ranges work and accuracy is within specs (triple checked against other known working 6 digit multimeters). Then after a while the value starts to shift, say 3.00006V input will become 2.88...V and then bang, all the ranges (except AC voltage and AC current) will show overload. Then after turning the power off for a while, then sometimes it will become sane again, and sometimes not.
I am suspecting that it is a stability issue, but haven't figured out the cause yet. Maybe even on the digital part on the analogue side. ADC seems to work just fine btw. The reason why I'm suspecting it is that Y463 oscillator amplitude is not perfectly stable although frequency 10.9MHz seems right. Also at some point I was seeing exactly 25ms period square wave coming out from input hybrid pin 10. Before this issue appeared then something whined briefly inside the unit when ranges switched. I didn't bother much, because everything was working, but it may have been that relays were not getting pure DC maybe similar to your case. Power rails seem to be stable, but -15V is a bit low, it's 14.5V while +15V rail is 15.06V or so.
I'm investigating it further... have you found a solution?