I can remember seeing some big machines using chains between the servo's and screws.These were bridgeports.
I don't think it would make much sense unless you know how to make them backlashfree wich is not an issue with the rubber tooth snare's.
I guess the stretching shouldn't be that much of an issue cause you should tension your belts and can do this as tight as you like and a bigger rubber snare would probably solve any strength issues.
sorry i can't help in actualy putting the chains to use.
just my 2p's