I know this isn't the popular answer but oh well. If there is one thing I've learned in my time in the military, it's that no one cares about you, but you. Do what's good for your family and yourself. Be a good bro in the sq, be upfront about your end goals and you should be gtg.
Caveat...I'm a little more jaded about the comfort and safety of the full time gig. I, and a few friends, have been on full time orders, that suddenly disappeared, and put us on the street with no back up option. In our case, all it took was a leadership change for things to be shaken up a bit. Lucky for me, I was single at the time. For the married guys, times were tough for a while. I'm now back in a full time gig, but I have less trust in its safety net and have an airline gig, just in case.
While this is going on, all our part-timer friends that had gotten their airline jobs, helped out. They have all been sitting pretty good, while we all take huge paycuts and sit at the bottom of a list. With sequestration and potentially more cuts (especially in the fighter community) I'm not as confident as I once was in the guard.
Personally, I would take the gig, continue to apply to the airlines and then make a decision. Most likely, by the time you get hired by an airline your 2 years will be up anyway. Trust me, big blue will not hesistate to cut those orders short if it benefits them.
As highdsight says, "have it your way." You've given your country 10-12 years their way. That's more than 99% will ever do, so serve on your own terms now. Having said that, if/when you go to the airlines/FedEx, don't be the guy that uses the "well...I make less money when I come to the mil/deploy," line. Get your sorties, deploy when it's time and enjoy the most fun job in the world.
Also, unless you're a patch, I would take a look at why a Hog unit has a full time AGR that they can't fill within the squadron. Nothing against you, but those are generally highly sought after by guys in the squadron. Some squadrons use them to attract talent, which is good. But in some squadrons that may mean an underlying issue in the squadron. Talk to the part-timers...especially the ones that used to be full time.
Goodluck.