Try this. Go find an old CD somewhere. Turn on your LED and observe its light as reflected off the recording side of the CD, which acts as a poor man's prism. If you look closely I'm betting you'll see the real cause of your fogging. When I did this using my 635nm red LEDs I noticed small, but very distinct, spikes of blue and blue-green light. That explained the light fogging I was seeing.
After mounting my LEDs under a single sheet of Rubylith the spikes, also as one would expect, disappeared completely. And so did my light fogging. As I've mentioned before, I then performed the pre-flashed paper fogging test (using Ilford MGIV FB/RC) and absolutely could not fog the paper even out to 60 minutes of direct exposure. I stopped the test as being pointless beyond that. Perhaps you could do the same or similar with Amberlith? Or the Roscoe filter described below?
This situation is analogous to the claims that the Thomas Duplex low-pressure sodium safelights fog paper because "they're just too bright." Nonsense. If the frequency range of the safe light being emitted does not overlap the paper's sensitivity range, the paper will not fog when exposed to that light, no matter how bright it is.
But the Duplex, like the LEDs, also emits at frequencies other than the (safe) doublet. These include numerous blues and greens, with one sizable spike just below 570nm.* Instead of using Rubylith, these can almost all be eliminated by filtering through an inexpensive sheet of Roscoe #19 Fire theatrical gel.** I've also done this in my darkroom and have tested a fully open Duplex using Kentmere Bromide graded paper out to 30 minutes with absolutely no detectable fog.
* See here for an example of a real world line spectrum of an unfiltered low-pressure sodium vapor emission formed through a 1mm slit. (Fourth item down the page, click on the third panel.) Note that everything to the left of that bright orange output (the doublet) is capable of fogging various b&w photo papers. Even though your unaided eyes cannot see them, similar outlying emissions can also occur with some LEDs.
** See here for a graph showing the absorption/transmission characteristics of the Roscoe #19 Fire filter.