Why wouldn't you treat the zener with beer?
Oh right
this is not audiophoolery this is voltnutting.
Anyway the 7071 zeners should have aged enough to reach 7081 levels of stability.
Just be warned: these meters take a VERY long time to reach sub ppm stability (~8 Hrs in a stable environment).
On the matter of calibration, there are a multitude of options just check the other volt-nutty threads here.
Cheapest would probably be to ship that meter to some fellow voltnut near you that has calibrated gear. (Dr. Frank maybe?)
On the other hand you can just ask some local cal-labs what kind of standards they've got.
Just write them exact instructions on what you want them do when asking for a quote.
(And if you sent it there, include a paper checklist type of document they can follow and put in measured values, greybeards love checklists)