I've learned that on days where a big screw up or crash happens, one just needs to shut the lights off and go do something else for the afternoon. My biggest screw-ups have always come on the coattails of a smaller one. Gets your head out of the place it needs to be and sets you up for disaster. Thankfully this is a hobby and we have that luxury.
Sorry to head about your lathe, chuck, and part. Hopefully they can all be fixed up. A new chuck is not the end of the world. A new decent quality import 6" 4J chuck would run ~$150 plus the effort to make a new backplate. A bit insulting to the ego, but far from the worst you could have done.