I have seen many of them with this fault. Interestingly enough, my experience is that the eray units (say in the 4 digits SNs) do show this issue pretty seldom, its mostly higher ones. Just my onbservation, but having serviced dozends of them. The drift rates I have seen was between roughly 1 to 20 ppm/day, so can get pretty dramatic, but can also be so low that you can essentially continue to use it (spec 0.43ppm/d). Important is to test over a couple of days (service note says 7). So don't test just a day, that will be misleading.
Re. the questions about custom parts (or custom selected), the 3458A has many of them, true, some being available, some not, just board level repair then, unless you have a donator board. Selftest not very helpfull, does not mean a lot if passed (as many sellers maybe think/pretend).
The Datron meters have a few custom parts too (mostly gate arrays, reference RN, transformers...), but here the issue is you cant get any of course. Display and also mechanical parts (posts) are sometimes an issue too.
The 7071/7081 meters usually are better to repair, most parts available, and straightforward technically. Even displays available. Underrated meter imo. But has its challanges (leakage, other stability issues; selftest is a good indicator though)