I wonder, is the LED sitting behind or within another glassy material, so the light emitted has to transmit through a volume, no matter how clear? If so, you may be better off eliminating this "clearcoat" or using a two-light setup. You keep your LEDs as you have it within this strip (if is modeled accurately like how a consumer-grade LED strip is made) but disable emit light. Duplicate and push these lights out so they're beyond the extents of the original geometry slightly. Check ON emit light for these but disable (uncheck) all of the Visibility parameters, including Occlude Other Lights. This way you can also tweak the strength of the original LEDs if they were too bright with Bloom/Glare, and you can always boost the actually emitted material if it wasn't bright enough before. It will be invisible in the rendering but it will fake your set up.
I do something similar for my street light fixtures that have LEDs or bulbs behind glass but I need the emitter object or a light object with an IES to drive the main light in the scene and the LEDs/Bulb to be the visible part.