I tried to do the TRT solo in 5 days last September, and managed about 3.5 days and 110+ miles before getting off the trail due to a painful bruised foot (?). It was a lot of miles (especially with shorter daylight in late September) to do day after day (33/mpd), at least for me. I did it very light in a Golite Ion pack.
I went counter-clockwise from Echo Lake. I resupplied at Kingsbury Market, and was going to in Tahoe City, but I bailed before then.
It's a great trail to do very fast with a tiny pack, and it's a beautiful trail. If you have time, do Christopher's Loop on the NE side and climb Mt. Tallac from Gilmore in Desolation. If you can avoid it, try to do the NE section on a day that DOESN'T have mountain bikes (every other day) - I hit it on a (yikes) Sunday bike day, and the amount of bikes coming down at me was insane.
Water was scarce on the E/NE side in September for sure. I got water at Star Lake, at Kingsbury Market, Spooner Lake, spring before Ophir Creek, Ophir Creek was running, then Gray Lake (GREAT water at spring coming into lake). Gray Lake is off the trail slightly - just go down to it, and then back up to trail on the other side). You'll have other springs, etc. running, such as water coming off Freel/Jobs Sister area, etc. But make sure to carry enough so you aren't pushing dehydration to unknown water sources, of course.
Have you done hikes of 30+ MPD before? For me, one day is easy, but 3+ days start adding up on the body, at least w/o lots of training ahead of time, or being part of a longer hike (e.g. PCT). Either way, take care of your feet!
If you have any questions about the trail, logistics, etc. I'd be happy to try to answer them - I also did the whole thing clockwise in 2003 (albeit much more slowly).
A few comments on your (great) geat list:
The bugs might still be out and even bad then, so be prepared as the threads above mentioned. With bad mosquitoes, I like to get indoors (e.g. Tarptent Contail), but with the miles you are doing, you'll be hiking til dark and turning in, so a tarp/bivy should be good. The bivy is likely pretty unnecessary otherwise - it might be summer thunderstorms, but most likely just afternoon stuff (not days of rain!). It's been thunderstormy lately. Your sleep/shelter system is light and looks good.
Montbell UL Down Inner Jacket / Hoody - Is this to help push your sleeping quilt down to a good temp? Otherwise you really won't need these. I hiked in September on both my TRT hikes, and only needed a Puffball vest and windshirt (e.g. Houdini). I find the windshirt is a great item for warmth early in the morning, against wind, anti-bug, etc. Very versatile.
Marmot Mica - If you go the tarp route, you could think about a MLD Pro PonchoTarp in the future - I have one and it's probably all the rain protection I need in most CA mountain conditions in the summer (and doubles as a tarp).
Compass - you won't need this. You can't lose the trail if you want (at least now that the snow is gone).
Ul utility cord for bear bag(25') - I don't bear bag up there, but it might give you peace of mind if you do. But I wonder if 25' is cutting it a bit close to being too short? Dunno.
Map - which map are you using? I like the one with the trail map on one side and the elevation profile, etc. on the other. Let's you know what kind of climbs are coming up, etc.