I think I may do a few games, a few RC segments, and a few of the wordier LR questions right before (maybe at 10:30am). I have found, thus far, that whenever the first section is LR, I struggle with the first few questions. It takes me a few minutes to acclimate myself to LR (hopefully this is unnecessary come June 11th, but even if it isn't this should help me), so if I do it beforehand, hopefully it will help get me off to a quick start.
Another piece of advice I've read, though not particularly related to the last day of studying, is to read everything you're given during that hour or so before the test begins (for June 11th, I mean the time from 12pm-1pm). People have suggested this to keep you sharp and on your game. I think it's something I'll try to do.