Hi,
I know this is a very old topic, but I'm wondering if you ever managed to solve this issue. I have exactly the same behaviour on my M-4650CR after making a measurement misstake (don't remember exactly what, happened more then a year ago) however if I measure the 1.2V reference voltage when the whole unit is assembled, it is 1.2V. If I power the board unassembled it is 1,53V as you mentioned in your findings. Checked everything else and I tend to think that it is the Maxim ICL7129ACPL chip itself causing the issue. I already ordered a new one just to find out, they are dead cheap anyway. But if you found another problem then I am interested to learn your findings. As you, this meter has some emotional value to me, already own it for about 30 years, and I would like to get it going again.
Regards, Alfi
PS: The measurements taken above that gave me the 1.2 volt were wrong, I was not measuring over the zener itself. So my conclusion here was totally wrong. It was indeed 1.53 volt over the defect zener.