How do they get more time out of you? Does the time spent as a GMO not count towards your service commitment?
You did Army HPSP. So you owe them 4 years. Will you not simply have 24-30 months left after you complete your 18-24 month GMO rotation?
It's complicated. Your internship year is obligation neutral, meaning it doesn't affect your payback in any way. Your resideny/fellowship, though, is 'concurrent payback', meaning for every year you do, you take one year off your pre-residency obligation and add one year to your post residency obligation. This doesn't add to your obligation... until your pre-resideny obligation reaches 0. Then you start adding more payback time. A GMO tour, therefore, means that some of the longer residencies effectively extend your obligation.
Examples
Straight through Training
You do 4 year HPSP, you now owe 4 years, you do a 1 year internship followed by 4 more years to finish up that Ortho residency. Your internship was neutral, you paid back 4 years of preresidency obligation and gained 4 years of obligation from residency. You now owe 4 years. Total time obligated to the service outside of residency: 4 years.
GMO and short Residency
You do 4 year HPSP, you now owe 4 years. You do a 1 year internship: you still owe 4 years because internship doesn't affect your obligation. You now do a 2 year GMO, you now owe 2 years. You do 2 more years to wrap up an IM residency. You paid back 2 years of pre-residency obligation and accumulated 2 more years of obligation. You now owe: 2 years. total time obligated to the service outside of residency: 4 years
GMO and long Residency
You do 4 year HPSP, you now owe 4 years. You do a 1 year internship: you still owe 4 years because internship doesn't affect your obligation. You now do a 2 year GMO, you now owe 2 years. You now do 4 years to wrap up an Ortho residency. You paid back your 2 remaining years of pre-residency obligation and picked up 4 years of obligation from the residency. You now owe: 4 years. Total time obligated to the service outside of residency: 6 years.
GMO all the way through
You do 4 year HPSP, you now owe 4 years. You do a 1 year internship: you still owe 4 years because internship doesn't affect your obligation. You then do a 2 year GMO, you now owe 2 years. You do 2 more years GMO (always an option, you never have to take a residency). You're done. You can do a civilian residency and use the GI bill to significantly increase your pay. Total time obligated to the service outside of residency: 4 years.
Keep in mind the GMO thing with a long residency hurts you even if you want to make a career out of the military: a major part of your pay as a career military physician is the bonus you get when you sign up for another however many years. If you're still paying down time, you don't get that bonus, so your pay is effectively lower than the guy who got straight through training even though you've both done the same job for the same amount of time.