It would make nice eye candy to display the voltage (especially if I make it adjustable) with a very affordable LED voltmeter like the ones on eBay for under $10. But will a part like that add a lot of noise to my clean DC? Most of them say 100K input impedance FWIW
It depends on the particular circitry of the voltmeter, but the amount of noise that can be reinjected in a decently designed PSU is much less than the PSU's self-noise.
The LT3080 has an output impedance of about 1milliohm, the voltmeter is 100 kiloohms.
Even if itwas capable of sending 5V spurious (assuming 5v internal rail, actually probably less), and it would be a serious malfunction, that would result in 50nV. Utterly negligible.
Actually, why do you want to make it a two-tier design? I believe the LT3080 itself is capable of more than adequate performance.
The real challenge here is the layout, with a strict hierarchical arrangement all the way.
The arrangement of the safety ground is not trivial.