[Catt]

This may sound a little blasphemous, but did you consider just calling the three-bet in the BB? CO is going to get all all his money in anyway (most likely) so you give up the chance to get an extra BB pre-flop, and in trade you (1) see if MP caps (and make back the 1 BB); (2) leave Button with the lead if you want him to have it (and he'll bet the flop almost always if it is checked to him), allowing you to donk if you like, or to have the chance to C/R the flop and face MP and all-in boy with two (presumably all-in boy calls, but you could knock out MP). I don't think I've been in this position with JJ and so haven't done it, but pretty sure I have with TT.

Post-flop, about the only thing I would do differently some portion of the time is to C/R the friendly turn -- but in so doing, I'd have to fold to a 3-bet. I'll often take the line you took given the prior streets' action.