Before going down the full adjustment route, if all you want is to check the readings of your equipment, perhaps something like the DMMCheck Plus would be a good tool to verify the reading of your equipment, and see how far off they are. It will give you spot check on AC/DC voltage and current, as well as resistance, frequency and duty cycle.
If they are within an acceptable range of your use case, then just note it and leave it, just apply the compensation to your readings.
If they are off enough to warrant an adjustment, then you take the next step. You balance the equipment needed vs. the cost of paying someone to do it, and make the decision. For the vintage equipment you have and the resolution they provide, you may even find the cost of adjustment way out-of-line and settle for the inaccuracy. You can make the call at that point.
If all you care about is voltage, then one of those Chinese voltage reference may do the job. I bought one out of curiosity, it came with a label with 6-digit voltage checks on a 34401a on all four voltage ranges. I verified it against my DMMs which have all been professionally NIST cal within the last 3 months, the voltage on the label are all within 34401a accuracy tolerance. The stability on the reference is good enough for a 4.5 digit DMM, beyond it, you will get jumpy trailing digits.
There are multiple versions that I have seen on-line, mine is the one with acrylic case, battery, and micro-USB charging port. The challenge for these Chinese references is quality varies greatly and it is hard to know what you actually get. That's why the DMMCheck Plus is attractive if you don't mind only having one reference voltage.
For the Keithley 177, those are $40-50 on the used market. Instead of trying to fix yours, you might be better off to get another working unit and use yours for parts. Or just use the BM869, which has a better spec anyway.