The practice of installing over-size tires, 750X16 and 820's has been around since the early days of hot rodding..
When traffic was lighter, and none of us had any clue as to what the associated problems caused by over-tiring a vehicle could cause, ignorance was bliss..
Large tires on wheels that are not designed to carry the larger tire, are one problem. The larger tires tend to act like big flywheels which impact braking and thereby reduce stopping distances..
Oversize tires can also come into contact with body/chassis parts, leading to tire failure..
A good friend of mine recently almost wrecked his '52 Chevy pickup. He put large bias ply tires on the rear to improve the gearing. I told him he might have made a mistake, he thought they looked cool..
A few weeks later I noted that he had new smaller radials on the truck.. Talking to a friend I found out that the guy with the '52 blew a rear tire on the freeway. One of the large rear tires was rubbing on the frame...
On the C-4 subject; Yes the C-4 is a 3 speed trans., they are quite small, therefore they fit into the X member frames nicely. The C-4 requires rear axle modifications, open drive line, springs and shocks. The easiest way to do this is with a later model rear end and suspension.. A more practical axle ratio can be used, something like 323/324 with smaller tires, maybe radials.. An added benefit would be the larger more modern rear brakes.
For my money it just does not get any better than a Columbia, they work great, and are correct for the car.. Ya know, if it ain't broke, don't fix it...