Need help on creating the most stable LED possible
Search for CC sink or source. Or use a LM317 as such from 5V for 20mA.
LED brightness is a function of current and long term, aging.
Voltage has a NTC so any temp rise will reduce voltage -x mV/'C so constant voltage or even PWM with CV will affect intensity.
Even temperature rise affects efficacy to some extent.
Consider multiple 20Cd &lt;=30deg  LED's operating at &lt;10mA. Consider temperature stability and short term aging or burn-in process.
Only use PD + R , not photo transistor and block all stray light.
What stability range do you need  from drift?  &gt; 30dB?   &gt; 60dB ?
How will you equalize emission curve?
Do you want to regulate output using dual PD detector in a  closed loop? That is best way.
One using beam split closed loop feedback, Two for sample output detector.     e.g. Using 1% emitter sample with fiberoptic.
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I assume using Bragg Effect... then get plots like this.

However I might suggest PNJ4K01F  or AMS-302 Panasonic logarithmic light detector with optical compensation...maybe for comparison.