Daisy, I calculated 27.2 miles from Shepherd to Kaweah basin: Shepherd - 10, Junction Mdw - 11.7, Island lake - 5.1.
You guys are gonna laugh, but one of the most remote areas pretty close to civilization is Versteeg lake (lake 3645 under Mt Tyndall). The only reason I knew about it was a couple of references in the HST fishing forum by a poster by the name of Ozark Flip:viewtopic.php?f=6&t=2295
I guess it's possible to come over the Tyndall/Versteeg mount from the Williamson bowl, but the easy way is to hike up from the Wright lakes. The thing is, not many people head into WLB - mostly because of Shepherd - and the ones who do are heading south toward Wallace/Wales/Tulainyo. But, if you head up towards Versteeg, there aren't any use trails, and definitely not any campsites @ 12k.
Shepherd is 10 miles, WLB another 3 over Rockwell, then just over 1 mile to Versteeg. This is what it looks like:
I caught a couple of golden/rainbow hybrids in the 8-9" range. I didn't stay long, but it's good place to get a fairly quick shot (you can do it in 1 day) of very high Sierra.