I can understand your reluctance to return it and go through the whole setup process again. As a frequent user of headphones myself, this is an interesting topic.
If you're up to it, it wouldn't be too hard of a repair. These phones appear to be very serviceable, which is another real plus to the Note 2. Try doing any work yourself on an Iphone or Ipod Touch and you'll know what I mean. Nightmare.
You can get the part super cheap and you don't even need to do any soldering.
Search for, "Samsung Galaxy Note 2 Disassembly" on youtube and you'll find some good instructional videos on how to take the phone apart.
Disassembly looks pretty straight forward.
Then search Ebay for "Galaxy Note 2 jack" and you find that you can get the part for just a few bucks! Can't beat that!
I say go for it. After seeing the innards of your phone, you'll get a whole new appreciation for all of the engineering that went into it. Plus, you'll probably learn a thing or two in the process and after fixing it, you'll probably get a good feeling of satisfaction. Sounds like a win win to me.