A punch, a Hammer and gentlemoderate tapping will likely put the zinc back in the water passage and out of the hole.
I wouldn't trust it to remain leak free, because that is the way my luck goes.
Or drill and re-tap.
Also FYI: sometimes a stubborn pipe fitting or bolt will break free it you try tightening it just a bit, like a 1/16th of a turn and then reversing. Sometimes it is required to do that several times with penetrating oil. Last resort HEAT and let it cool. tips form my brother who is a retired union pipe fitter
