I was thinking of starting a thread on it the other day
My thoughts on this are to use rechargeable batteries, stored in the same heavily shielded metal enclosure, alongside the reference, like in a Fluke 732. For the batteries, something practical with lots of energy and long life, like LiFePo or LiIon. I do not know what kind of noise these have, if lead acid has lower noise, that can be an option too. Keep two independent battery banks, one that is being charged, and one that is used to power the reference. As one bank is completely discharged, you switch over to the other bank. That way you remove any noise from ever entering the system from the outside, with runs with the assumption that the batteries are relatively low noise.
For regulation or step down to a practical range, I was thinking of a simple npn - zener regulator, using a low noise zener diode (1N5518, 1N5519, 1N5520, 1N5521, 1N5522, 1N5523). Another option that could be great to try is using the LTC6655 low noise reference. It could also be used to reduce the noise of the LT3042, which on its own has something like 10uV of noise 0.1 to 10Hz, and 2uV of noise 10Hz to 100kHz.