Given your situation, I'd say:
Ride the road bikes and pack very light or use a trailer if you carry a bit more. Get lower gearing though.

If you decide to buy bikes and are on a budget there are a number of good choices for $599 to a bit over $1000. I like my Windsor Touring ($599) just fine. Three of us rode them across the US and were happy with them. The REI Novarra Randioneer, Fuji Touring, LHT, and a few others are also good choices, but the cheapest is to ride what you have. I would not find the geometry or riding position to be a problem, but others might.

I agree with Foamy that you should buy food daily or close to daily. No way you can carry a lot of food and pack light enough IMO.

Free camping should be easy to find most of the time if you avoid bigger cities and stick with smaller towns. In the middle of the country almost all small towns will leave you alone if you camp in the little town park. Ask around if in doubt, you will generally be able to camp in the town park, a church lot, or someones yard. Cashiers, librarians, the police dept or sheriff's office, city hall, the local church, or the local fire hall are all good places to ask where you might pitch a tent for the night.

If you use an Adventure Cycling Route for some or all of your route many free places to stay and contacts will be listed on the maps.