Yellow would probably look nice, but I already used yellows for the middle of the LL square, and I needed something to contrast against the rings. The shine was already white in the default logo, so I kept that, and then made an alternate one that used all of the Olympic colours in a gradient.
Here it is, using a shade of yellow that's slightly off the official Olympic shade so that the ring and triangle would still stand out:

At this point, it looks like white is probably going to be the best.