Carmageddon really cannot handle latency. It doesn't alter the fact that because of the type of game it is, Carmageddon will always have problems over the net. The cars move a long way in a short time, so a comms spike would totally mess up the game. The characters in Quake, for example, don't move so quickly. You might get rammed and wasted by dumpy before you even knew he was there.
Exact position is vital.
That's not the case with Carmageddon. After a ram, the cars bounce off each other. If the cars are not in exactly the same position on each computer, they will wind up in totally different locations. The game will get badly out of sync. Prediction code is of less use since what happens is so dependant on exact positioning.