Do you have any other meters approaching 5.5 or 6.5 digit capability, or precision resistors that have a tight tolerance that you can use for future referencing, or a work bench that can be made to operate within a few degrees of 23C for long periods ? Can you borrow someone elses 5.5 or 6.5 digit DMM for round-robin comparisons ? There are many ways to grow your confidence in the readings a meter can give at any point in time for any particular range.
In your situation where you may be able to get a deviation report, then imho additional value can be gained in quickly using your meter to transfer measurement levels to other parts such as reference resistors or other similar meters, or diy voltage and current references. That benefit is improved if you have a controlled temperature environment for testing, and controlled test setups such as leads and burdons that emulate what the test house may have used, and already prepared reference resistors with 4W terminals, and prepared voltage and current references. I've recently taken that path with a repaired 34401A. No single 'calibration' report is going to have long-term benefit, but spreading out your measurements over multiple parts/devices should provide confidence going forward that the 34401A is not significantly changing for particular ranges.
It can take time and effort to build up related references/meters that can be used to complement a 34401A, so you may want to consider that preparation before paying for a one-off report, unless of course you plan to pay for such reporting on a 1-2 year cycle basis. If you do plan on getting regular reporting, then using the same test house and spreadsheeting actual measurement results can give confidence on how your 34401A is aging, and allow higher confidence in assigning adjusted measurement values to reference parts.