"but Kings Canyon National Park is the most spectacular part of the High Sierra"
Only if you've had limited exposure to Sequoia NP.
"does the first half of the High Sierra Trail and then circles the magnificent Kaweah Peaks at the Kings Canyon/Sequoia National Parks border. Starting at Bearpaw Meadow or Wolverton, hike west on the HST through Hamilton Lakes (this is another lake setting that competes with Rae Lakes) and down to the Kern River. Left/north onto the PCT/JMT for a few miles. Next, you leave the HST/PCT/JMT and turn left/northwest onto the Colby Pass Trail. This will take you down Cloud Canyon. Next, sharp left into Deadman Canyon and over Elizabeth Pass. Spits you back onto the HST and back to your trailhead. If you do this loop, you will get more reprieve from the crowds and the heavily impacted campsites of the John Muir Highway."
A much better choice than anything on trail in Kings Canyon, IMO, but the reference to PCT/JMT in Kern Canyon is incorrect. They parallel Kern Canyon about 4 miles east of the canyon in that area. The trail you would be using is the Kern Canyon Trail
An equally good choice would be Elizabeth's first suggestion, i.e. Roads End, Avalanche Pass....Colby Pass, north in Kern Canyon and on to Lake S. America...Forester Pass and back, especially if you will need a resupply(see below). You haven't stated how many miles you expect to hike per day, or I have missed it. If you can do 10 miles/day there should be no need for resupply, and THAT will enormously simplify your trip. In fact it is about the only way to make a go of it, IMO, unless you have a lot of time and energy. Both of the above routes, if resupply were necessary, would require a side trip over one of the East Side passes, most likely Shepherd. I think you would find it very difficult to hike out over Shepherd Pass, on down to Independence, then back up over Shepherd Pass and continue on over Forester Pass, assuming you choose the Roads End route. You would be looking at a minimum of 3 extra days to accomplish this. In the case of the first route, above, resupply would for all practical purposes be unfeasible due to the distance from any source of resupply. Check it out on your maps, and I think you will see what I am talking about in both cases.