The circuit is practically identical to the good old Geller SVR.
The standard is highly immune to changes in humidity, if built in a gasket sealed type enclosure and o-rings fitted under the binding posts. There is also space for a small silica gel bag (on the solder side of the PCB between the binding posts).
The geller SVR lacks of EMI-Filtering at the output.
I would use a 10-100nF capacitor at the output if the reference is stable with capacitive loads. (most are).
Humidity can only avoided by using a reference with hermetically package which is mechanically decoupled from the PCB.
All other measures do only increase the time constant. (from days to weeks).
But since humidity changes seasonal. You will have different output values in spring and autumn.
For most references a stable power supply is also essential.
If I would build this I would probably use 2 9V Blocks (no EMI from power supply)
+ a 15V regulator built from a LT1763.
With best regards
Andreas