Over tightening the chain is unlikely to damage the rubbers. What may be damaged are the chain, the gearbox and rear wheel sprockets, the rear wheel sprocket carrier bearing and possibly the rear wheel bearings themselves. It would be wise to carefully check all of these and replace any that are showing signs of wear. Hopefully the gearbox sprocket bearing is OK as this is a big job to replace. The cush drive rubbers will wear and can be replaced or repacked with something like pieces of inner tube glued onto the old rubbers as long as the old ones are not breaking up. I'm not sure what you mean by the "3 second delay before the drive picks up"?