I'd be somewhat surprised if the newest can't take a 28c tire, have you tried them? If not carrying a load, I make my kids carry a small one, I would think 25c could be fine. Remember that he's probably small enough that the pressure of the tire should stay low which will keep the ride more comfortable. Although I haven't done the TransAmerica, as a 13yo I rode daily on rural country roads, the kind that get resurfaced every other year with a fresh coat of oil and a layer of gravel not to mention the seasonal highways. I did it with 23c tires and never had a problem with grip as long as I didn't take sharp corners faster than 25mph.
As for load for my kids, I bought the rockbros seatpost rack and the bag that goes with it that has mini-panniers that look like side pockets till you unzip them and let them drop. Upside to the bag is it also has a mesh pocket for a 3rd water bottle, your kid's bike can probably handle 2 bottles while my kid's could only take one so I found that very handy. I made the oldest two carry their water, snacks, spare tubes, CO2 cartridges, and rain coats. Because of the way we toured, the equipment was moved by car each day, so I didn't have them carry clothes on the most recent trip. On a previous one I also added 2 days worth of clothes to the oldest's bag, and she had no trouble with that, she was only 9 at the time, so I would think a 13yo could handle that much and it'll be that much less for you. A seatpost rack can only handle 20lbs, not too bad for a kid and a nice bit of weight off the burden you'll already have.