Re: Broken p-trap
I ended up cutting the tailpipe closer to the wall and I found the clog inside there. The rest of the pipe closer to the wall was in good shape. The 1-1/4" flexible Fernco coupling I tried wouldn't seal around the copper waste pipe from the wall.
I eventually assembled an ABS p-trap and connected it using ABS adapter fittings. Had to get a new sink drain too.
Seems to be holding up well so far. This sink hasn't drained this well in years. The bathroom needs to be completely redone anyway so I'm thinking of this as relatively temporary.
Thanks for everybody's insight and suggestions.