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If the key objective is climbing Whitney, then Kearsage Pass to Whitney Portal is great (we did it last summer: viewtopic.php?f=1&t=8265), but doesn't have too many options for doing a substantial portion off trail, other than day hikes to nearby peaks or basins like Wright/Wales Lakes. The first day to Kearsarge Lakes isn't too bad if you acclimatize by camping at altitude the night before.
Kearsarge to Whitney seems like a good fit for older, experienced scouts. There are in fact some good off trail options that would make for a memorable adventure. After Forester Pass, the kids could do a loop into Milestone Basin, in the upper reaches of the Kern watershed. There are trails here, but plenty of options for off trail hiking and peak bagging as well.
Another option is to hike into Center Basin, over Junction Pass, and then over Shepherd Pass. This avoids beautiful Forester Pass, but sets the kids up for some memorable peak opportunities -- Mt. Tyndall, Junction Peak, Diamond Mesa, Mt. Williamson. Most of this route is trailed, but it is lightly trafficked compared to the JMT.
Don't let anyone talk you out of The HST start at Crescent Meadow. The first day is not a slog; less than 2000 ft total gain to upper Hamilton (14 - 17mi, depending on which calculator you believe) most of it very gentle, and surprise views around every turn with increasing spectacle as you go, especially the approach to Valhalla.
For a good dose of crosscountry, side trips to Eagle Scout and Black Kaweah from upper Big Arroyo should satisfy. Problem with the other passes - Pants and Pyra-Queen - is that they cut the heart out of the trip: Big Arroyo, Moraine Lake, Kern Canyon. Second consideration is that W to E is the hard way for these: Pants Pass is so-called because that's the typical way down E to W. It can be done, but if its beyond just one of your group, you have to retreat the whole route, whereas a side trip summit or two doesn't risk the whole itinerary.
