See if you can switch into the reserves to finish out your service obligation while in med school. Depending on where your med school is there may be some guard units close by that would take you. Not sure how feasible this is, but worth looking into. Could also go ahead and apply to med school, and then if accepted request that they defer your acceptance by a year (have seen them do this for an officer that the Army didn't want to give an HPSP contract to because they wanted him to stay in his primary billet). If not accepted, then continue with your plan to make yourself more competitive for the following year.
I have also seen people do something to get out of their enlistments early. Not sure what they did, and it was in the Navy, but one E6 corpsman with about 11 years of service just decided one day she didn't want to do it anymore. I think she had another 2 years on her enlistment, but she was able get out.