You are right, but unfortunaly a 34401a is all I have at home, and don't have the money to buy anything better. I wanted to get the best accuracy possible.
You should start by understanding what is possible and what is really not practical. There is a reason the tolerances in meters are often referred to as 'uncertainties'. You can dial your meter in all you want relative to a calibration report or some standard you may have, but you're probably not be improving anything and you just won't realize it because you have no way of knowing. And without knowing the details of your economy calibration lab, deciding how to improve on things would be sheer speculation.
First, a properly working 34401A is a pretty accurate meter just by being within its stated specifications. Precision and accuracy become insanely expensive beyond that point. Trying to do better than what it is specified for is not a casual endeavor that is likely to turn out well for someone with limited resources. I'd be curious to know exactly why you want to do this.
Second, in my limited experience with them the primary driver of uncertainty in these seems to be temperature. You can plot out the readings over a 4 hour warmup period in a room with only moderate temperature control (a heated house room, for example) and you'll typically see 10-15ppm change over that period and 2-3 ppm changes with room temperature cycling. Low TC systems are difficult and expensive to make and 35ppm basic accuracy is actually quite an achievement. Simply dialing your meter to some exact number under one specific condition--even if you had a perfect standard--isn't going to result in a perfectly accurate meter going forward as conditions change.
Last, before you do anything you need to know what the capabilities and uncertainties of the calibration lab are. If this is a budget calibration, there's a good chance that the results you get may not be all that helpful.