Hey Blake,
My bro was a scout leader for a while and did two of these so he asked me for a lot of input in their planning.
Before I mention anything about actual routes, there are a couple of big pieces of advice I have.
1. Absolutely DO NOT have a big first day, especially if it involves strenuous elevation change. You might already know this, but a lot of people get sick of they over exert at that altitude before having a day to acclimate. This can linger for days if it hits them. I speak from personal experience and the stories from my brother on their first outing. Think boyscouts puking in the trees and not able to eat after a big first day.
2. Planning on a certain amount of your mileage to be in the form of day trips on the side is not a bad idea. It makes it so you can plan more like a 35-40 mile trip and get those last 10-15 in along the way without all the heavy packs on which means happier scouts.
So with that said, and the fact that you want to do a route that involves a shuttle, the possibilities are huge. The central Uintas are a good spot to look and you can setup relatively short shuttles. I believe one of the trips my bro did was From Center Park to Swift Creek. That's one of those ones where the route itself is only like 40 miles but with a day to bag King's and maybe something else, the 50 mile requirement is easily met. I just quickly drew it up on Google Maps which pegged the core route at 32 so accounting for the broad lines and the fact that I didn't try to follow the trail, it's at least 40 miles. It's the blue line here:
View larger map.
Shuttling those two trailheads would be relatively easy although I think Center Park requires high clearance. I wouldn't start at Swift Creek because of big elevation change the first day. Start at Center Park because you already start high and it will give the boys a chance to acclimate.
The red line on that map would be a good route for a straight point-to-point where you'd probably rack up your miles without any side trips. I think google said 40 for my line so most definitely 50. If you have the Probst book you could figure out decent mileage but keep in mind that most distances in the Probst book are short by a bit. They must have measured with a string on a map or something because whenever I track my GPS they are always about 10-15% short of the actual mileage.
Do you have the Nat Geo Trails Illustrated for the Uintas? If not I'd pick one up ASAP. Its a great map for figuring this kind of stuff out and truthfully, you could basically pick two trailheads and put together a 50-miler in almost any part of the Uintas. If you have specific questions about any certain areas or trailheads and such I and others here are pretty familiar with most of the range.