Yes, somehow duck tape should be able fix this little problem. Maybe it could be used like hardfacing. You know, like built up the rails a little wider for the damaged chain to run in. The duck tape queen shall triumph over the evil chain.
I would use the purple tape in this case. Purple is a calming color. Seriously, I just did another session of filing, and I think I'll try to crank it up tomorrow, when the emergency room might be better staffed. I don't think it will turn yet, still seems a little stickery.