So I finally got around to trying out what I hoped would be the ideal solution for replacing the CFL with LEDs in my Game Gear: using an opaque white straw as a diffuser tube for the two side-mounted LEDs.
The outcome was unsatisfactory.
If you recall, I had previously tried a frosted "clear" straw, with very small (if any) improvement over the exposed side-mounted LEDs. I had hoped that an opaque white straw would make the lighting more even across the screen and, by filtering the light through the white plastic, might also mimic the white CFL coloring more.
My theory actually did bear out, to some degree. The "hot spots" on the side of the screen near the bulbs were much diffused, and the coloring on the screen seemed more closely matched to that of a "stock" Game Gear. But the screen was dim. I found I was caught between a rock and a hard place, where either I could have a) the color and lighting to be somewhat natural, but the screen would be really dim and you'd have to hold the system at a 45 degree angle, or b) the screen would be *almost* bright enough (it never quite reached the appealing luminance of my good condition original system) but would be utterly washed out.
I didn't even bother taking pictures - it just wasn't worth it. My conclusion is that the LEDs couldn't come anywhere near reproducing the CFL lighting when filtered through an opaque white straw.
Someone suggested carefully using the original glass of the CFL bulb as the diffuser tube in the comments on one of my earlier posts. That would be super interesting to try, and may be the best bet in the end. But for the time being I would say the best implementation with two side-mounted white LEDs is with a frosted clear straw as a diffuser (per THIS POST)