The main problem with using the AMT 1960 C10 chassis on anything later than 1964 or so is that it has a torsion bar front suspension. The trucks switched to coil springs later on.
'63 was when they went to coils in the front. There's actually considerable differences in the frames from the '60-'62 and the '63-'72, about the only thing that's really the same is the rear suspension and maybe the spare tire carrier. Even the rear axle is different, with the '62 and earlier using the Eaton HO33 axle and the '63 and later using the GM Truck 12 bolt (note, this for Chevrolet only).
If you can find them, Zee/Zykmex made some very decent 1/24 motorcycles back in the late '70s to early '90s. Mostly street bikes, but there was some very nice dirt bikes, too, plus a few bicycles and atvs. I'm not sure who has the tooling now, but their stuff has been repopped a few times since. Their Harley Chopper, basically the Captain America bike from Easy Rider, seems to be the one I've seen reissued the most. They pop up on Ebay from time to time as well, but can get a little spendy.
Also, the Henderson mentioned by Randy, which I think may have actually been in the Gangbusters '32 Chevy rather than the Chrysler, is available in resin from Motor City Resin. I've seen one in person, very nicely done. They also offer a side car to go with it.
I prefer using laminated pieces, too. I've found that sometimes, the thickness of the rails will be a dimension not available in rectangular stock or tubing. By laminating it, I can control the dimensions. Also, you will want to either pin the extensions or make some sort of locking key in them to maintain the structural integrity.