Well, the PCT from Tuolumne north to Sonora Pass is very nice. I'm guessing that's 70 miles? There is a surprising amount of solitude to be found on that stretch, too. Some of the very best spots along that stretch are 1/2 mile to 3 miles off-trail: Rodgers Lake (west of trail near Smedberg) and Bonnie Lake (north of trail at northern Yosemite border) are both Can't Miss.
I don't find the PCT north of Sonora Pass, nor the Lake Tahoe area in general, nearly as scenic as the JMT. Maybe that's just me - I prefer the High Sierra, am not as charmed by the gentler terrain north of Sonora Pass. Of course, not everyone would agree with me here. As for the TRT, maybe save it for a separate trip? Coming directly off all those remote miles on the JMT and/or northern Yosemite, the TRT may seem entirely too close to civilization.
If I had your schedule, I'd add ~3 days to my JMT schedule by dilly-dallying in the Tuolumne to Reds Meadow section and the Silver Pass section that follows. (I only choose those sections over the ones further south because the interval between resupplies is short, so adding a day or two to a section isn't a big food burden.)
Tuolumne to Reds is brimming with amazing side trips to/along some of the most fairy-tale lakes in all the Sierra. It is a total waste to rush through here in 3 days like most people do. You can visit Lyell Glacier, Lost Lakes, Marie Lakes, Davis Lake. You can walk to the northwest end of Thousand Island Lake, and from there, hike to Catherine Lake (more ambitious) and/or over a very easy saddle into the watershed above/to the west of Garnet Lake. That is a freaking gorgeous place, with Banner Peak towering immediately over. A little south of there, detour from the JMT to camp at Ediza Lake and do a dayhike to Nydiver and/or Iceberg Lakes. In fact, once you get to the Shadow/Ediza Lakes area, a most interesting way to finish up is to skip the JMT in favor of the x-country loop from Ediza to Iceberg to Cecile to Minaret Lake and out to Reds Meadow via the Minaret Lake Trail.
Reds Meadow to Edison Lake or Muir Trail Ranch takes you over the Silver Divide, a colorful and generally stunning area. A ton of lakes up there, and I don't know them all so well, so maybe someone here has a specific suggestion for day-exploring. Another option for a side-trip along the Silver Divide is to leave the JMT at Tully Hole, hike east up the McGee Creek Trail to Tully Lake. Once at Tully Lake, hike due west up a gully to find a wonderland of lakes, ponds, and huge metamorphic-rock mountains reflected in alpenglow. Some of my best photos anywhere in the Sierra are taken from that spot.
If you are resupplying at Muir Trail Ranch, you can stop to explore the Selden Pass area or even check out the Italy Pass trail. I don't know this region so well.
Exiting the JMT at Whitney, it'll be easy to find a ride into Lone Pine (just talk to some people you've met on the hike that day). Bishop is a nice overnighting place for resupply. Then hitchhike to Tuolumne Meadows and hike north on the PCT till you run out of time.
I think it's pretty easy to hitchhike around the Sierras, especially the Eastern Sierra.