Wow, Terry! That's quite a story. There has been some strong discussion regarding Scouts and their behavior on trails. I'd put your troupe and experience on the negative side of the card.
There are others here who are scouting leaders, and they are the opposite: Fantastic leaders, and know about keeping the group together, as WELL as the proper acclimation for their scouts.
Since your younger son has demonstrated a serious negative reaction to the altitude, it is imperative that you get him to altitude and spend TWO nights at the altitude BEFORE you start hiking. The best recommendation is to drive up to Horseshoe Meadows (south off the Whitney Portal road) and camp there two nights. Elevation is 10,000, walk-in campground usually has ample space. It will get your son far better adjusted to the altitude than anything else you can do. Here's a thread: Trail Peak: Warmup / acclimatization hike
Also, go to your doctor and get some Diamox. 125 mg once or twice a day is the recommended level for the altitude. Do NOT take higher doses. Start it the day you start the acclimation process.
Keep the jackrabbit urge in check. Slow and steady will help prevent the exhaustion that can really increase the altitude issues.
Drink drink drink! About a pint an hour. 2-3 liters should be carried from last water spot (Trail Camp.) Some electrolytes will help. Urination should be every few hours, and should be clear. Snacking often, especially lower on the trail is good. Appetite could disappear as you get higher, so food in the belly earlier is good.
I like your 3 a.m. (or later) starting plan. You could camp at Horseshoe, and still drive to Whitney Portal that morning. Drive time is about 40 minutes.
I hope more people will add their input here...