Highly accurate constant current source
I can speak from some small experiences on a part of this. I'll leave the "highly constant and highly stable" current source design to those who know this better than I. But I was involved in creating LED-based light sources intended as "lamp references" for optical work. Your description suggests the same to me.

(1) Even if you have a perfect current source, LED output varies with temperature. So they must be operated at a stable temperature. We chose to heat them to about \$75^\circ\text{C}\$ using a closed loop control. That solved the temperature drift problem.

(2) LEDs themselves aren't consistent. Even those cut from the same wafer aren't consistent. We had to pre-stress thousands of them, holding them at a stable temperature while running them with a current source for days. We monitored the optical output and data logged the results. A few, a SMALL FEW, would actually gradually drift and then settle down to a stable spot (peak wavelength and intensity.) We chose those for the standards. We threw away most of them, by far. At the time, we kept less than 1% of those tested because more than 99% of them simply weren't stable even over periods of hours.

I'm just saying. I believe you are focused on the wrong issue. Buy yourself a really nice 100ppm "stability" current source from a supplier that provides the range and resolution and accuracy you want and guarantees all of it (it won't be cheap.) And then use that with your LEDs and play around with temperature and various LEDs just to sample the modern situation with LEDs before going off and worrying about the current source end of it. You need to know what parameters need to be placed under your control in order to meet your requirements. Dog first, tail later. Just one opinion.