... Also the 7815 wants a minimum load of 5mA and decoupling caps.
Considering this, then you have two choices. (1) put a load resistor at the output of the 7815 to get it to draw a constant 5mA, or (2) don't waste a 7815 and simply use a 15V zener diode drawing 5-10 mA of current instead. Here's why a zener will work: The line regulation of the reference is 0.002%/V, which put another way means that an input voltage change of 1V causes .002% change in output of the reference. The reference is 0.05% initial tolerance. If you don't even calibrate the PSU output, you are still going to be well within 0.05% even if the zener cannot hold its output stable +/- 1V , but it can do much better than that. The load for the zener regulator is only the reference, and it is going to be a relatively constant load at 1 mA or so (and the load for the reference output is only the input of an opamp which draws very little current). So the zener regulator will not see much load change, so it's voltage output will remain relatively flat. Most zeners can hold within a few hundred mV over a 10 mA load change or so, and this application will see very little dynamic load changes at the zener regulator output. Even if it DID change by 10 mA, the zener voltage will change by about 100 mA or so, and that will result in just 0.002% of that getting through to the reference output, or just 2 uV of output change in the reference. It's insignificant and within your error budget.
As for the input to the zener regulator, a quick simulation showed that even a 4V input change, dropping the input from 22V to 18V, which can happen under heavy PSU output loads, caused a change in the zener regulator output by just 200 mV. This will be seen through the reference at 0.002%/V or just 4 uV of change in the reference output voltage.
My point of going through all that is to show you that a few observations and calculations can determine that a 7815 is not really needed here, and a zener is good enough for pre-regulating the reference input voltage. Remember, the reference itself is already a voltage regulator.
I just used a 1K resistor in series with a 15V zener, to get the most basic 15V zener regulator. You can do better, but it's all overkill.