LEDs are no good for GI - the main reason is that they are too directional and for GI you need a more generous spread of light.
This criticism and that the leds are too white is often made. I wonder exactly which leds people have used - they all seem to be lumped under the same de******ion as "leds", but there is quite a variety. I see that cointaker have some 170° warm white ones that I've wondered how they'd go behind a BG or big bit of plastic. I like the idea of reducing heat on BG.
I wonder if a led controller to turn them down a bit might help - not that easy to do as these normally control leds in series strings, whereas pins use parallel strings for GI. I also wonder if a sheet of diffuser between leds and backglass might help, maybe something as simple as tracing paper. I've also heard, maybe on this site, of people sanding the led surface to difuse it some more.
It is possable to make a unit to adjust the brightness of the leds, I wonder how many people would be interested in buying them if someone made a "plug and Play" type of dimmer with a trimpot you can turn to change the brightness?