LEDs with highly stable spectrums
It might be better to talk to an apps engineer at the the company that makes your LED's.  there are several mechanisms possible that will cause wavelength shifts and unfortunately the solutions are often are at odds.  HEre are some scenarios and possible solutions:

1) if it's a heating effect and wavelength is shifting with atomic spacing change then PWM might be the way to go.  BUt this would manifest itself as a broadening of the spectrum, you seem to be getting peaking at certain wavelengths.  The activation energy of that subsidiary peak should tell the manufacturer something.

2) but the effect might be from ballistic transport of the carriers which are then causing spectral spreading collisionally - in that case a DC approach would be best as you want to avoid current spiking.

3) higher current means a larger volume involved with conduction which means a greater chance of interacting with dislocations and crystal defects and traps.