I can't believe I'm doing this, but...
The thing about the hanging rope... Assume the standard "plan the length of the rope for the hanging" work was done. That setup was for Barbie. So the rope was not cut to length for a proper Jim hanging... the writers could always use that as a built-in excuse for why Jim's neck wasn't broken. Also, Jim put the noose on himself. Normally someone else puts the noose on... so Jim could have put the noose on in such a way as to inhibit the automatic neck snap, and combined with the improper rope length, you get the scenario that played out.
That said... he still should have had a very sore neck, probably difficulty talking if not a crushed larynx in the process... and I don't even recall seeing much of a bruise afterwards... so they still fail even with my possible explanations.
Yeah baby! It's Halloween!