That's an awesome observation. With Cherry you could get a very thin, sleek car and still keep a lot of density, and not worry about thin areas breaking out. Much slicker than my pocketing in old lead strip weights for mass!
I think you are on the right track with the wheels. The stock plastic ones straight out of the package had a thin ridge of mold line on the circumference that looked to affect roundness and performance, and the "nails" were pretty loosely fit to the holes. Truing them up and making better axle stubs than the nails is probably where all the speed will come from in the design. That and in the machining of the body you can make sure the grooves underneath for the stubs to mount in are truly square and parallel! Don't know how close they really are in the stock pre-cut pine blocks, as I didn't know what a micrometer even was when I was twelve, but they did seem pretty suspect even to us kids as some cars definitely did track a lot better than others.
Thats awesome they have a dads race now. Bet that adds a lot to the fun and removes some of the problems, too. Good luck!