Just a comment. Riding across the US, thousands of miles, day after day, takes quite a bit of desire. The physical side is no big deal. But to suggest to someone who is not a bicyclist to ride across the US, thousands of miles, day after day of riding, is maybe a bit naive. You have to want to ride your bike before starting such an undertaking. The people you are talking to probably have not ridden a bike since childhood. Almost certainly are not frequent recreational riders who enjoy riding a bike. Why would they suddenly have the desire, motivation, want to ride a bike for thousands of miles, day after day of riding? Again, the physical part is easy. You see bicyclists of every condition riding. But they want to ride, obviously. What are you going to do when some or all of the people you take with you decide not to ride any further? Its also highly likely that the people who would be willing to actually do the cross US ride are the ones who will not relapse anyway because they already have the motivation, drive to succeed once they got off the drugs/alcohol/etc. So your ride will not really benefit anyone because the ones who will relapse won't ride and the ones who do ride will not relapse whether they ride or not.
My suggestion would be to do a loop in Ohio. A week long ride. Long enough to get submersed in bicycling, but not so long that initial enthusiasm will fade. Just do it as a way to introduce good exercise to the people. Have them experience the joy of riding a bike. That's enough. Not as some grand life changing thing.