Which branch of military service would allow me to work on my MOS or rating?

Yes you will do your job (depending on the job). MOS's merge and delete all the time, if your job is contracted to civilians, so sorry charlie, you wont do your job. I know a tank turret mechanic, that has been in for 6 years and never touched a tank. He works in the training room and pushes paper. Other MOS's always do their job, like medics and 11B. (lol)