thing is its bent and you can only do the best you can with it and hope for the best -- for all you know you may get a good jack and still have the same issue with it ??? no telling . maybe in the female part of things ???
with out a back up part or another known 100% works fine headphone to try its all just a best guess
Sure the crackling is coming from the connector and cable. It always happens to any pair of headphones. That's why I always recommend staying away from the bling bling beats and BOSE headphones and going with quality studio headphones like Shure, Seinheisser, AKG, Sony, etc.... Many of those have removable cables. Just unclip it from the headphones and get another 3.5mm cable to replace it for $5 in 5 seconds.
Without a removable cable you have to dismantle the headphones and solder a new cable on.