I have not personally been in this situation, but I've never heard of someone carrying out a successful swap for orthopaedics. Nothing is impossible, but you'd have to have a compelling reason. Having some exposure to a similar problem I can tell you a few things. As for not wanting to destroy relationships with the program, the reality is that you'll have to confront your PD or chairman at some point. With only a couple months remaining in the academic year, I would make a game plan and do it this week.
HOwever, I would be ready for some tough questions. It's not just as easy as changing call and rotation schedules. It's a lot of extra work and a pain in the rear for your PD and chairman and hospital to do this for you. You will have to answer some tough questions: Why can't your girlfriend move here? If she's that important why aren't you engaged? Is there some end-of-life or family illness for which you need to move? Is there no other family that can take care of these issues? Why did you rank us if you absolutely wouldn't want to be here? Is this something you could have anticipated before the match? Is this due to something that came up after the match? Are you depressed being here? Have you seen a psychiatrist? Are you just having a difficult time adjusting? Do you need to just take some time off? Is residency a priority for you? Have you thought about another career? What about another specialty?
I'm telling you, just be ready!
Furthermore, you'll first have to find someone willing to swap- your PD isn't going to take that pressure on himself unless it's an emergency for which you're leaving. You'll each have to be willing to travel for an interview likely midweek, take time off your current rotations and have others cover your call. Also, the hospital may not approve it or they may opt to save money and say you can let your resident go but we're not going to accept someone in his place.
Keep in mind that your PD and chairman trained during the period of no work hour restrictions and like most from that era think we current residents are weak and complain, feel entitled, and will never walk to work and back uphill both ways in the snow like they did. Bottom line is, you better have a valid reason to move other than wanting to be close to your family and girlfriend. At least if you're married, AND your wife can't move for some reason, you can say your wife doesn't want to wait 5 years to start a family, that's actually a decent reason. But if you're dating, you prob won't get married for another couple years and the earliest you'd start a family would be your chief year, so not a compelling enough reason.
Anyhow, just some food for thought from my (not personal) experience. It's not worth discussing it with your PD or chairman unless you've got everything in place and most importantly, a solid reason for needing to move.