always put a nut on before you put on the puller. that said take a die and break it then put it on below the bad threads use a vice gip to hold it together and turn it off. may take a few times.
Using a broken or 2-piece die would be my preferred approach if only the top were mushroomed. Be sure to put die upside down. A thread file would be next.
For really ruined threads, I’ve wondered about cutting off the male threads and drilling/tapping for something like a 5/16″ grade 8 bolt. Would it be safe? I don’t know. If the crank threads have been hit really hard one has to wonder about other damage.
am