I have been an EMT for 6 months after spending 6 weeks of my summer doing an accelerated program. I got hired the day after my National Registry exam. I work 30-50 hours a week while going to school, they work around my schedule, I have a lot of down time, I still see some freaky things, I get AMAZING patient interaction experience, and I get to be the highest level of care for people for part of their crisis. I will be working as a hospital EMT and an ambulance EMT ~80 hrs a week during my year off. It has been the single most solidifying piece of the puzzle towards becoming a doctor. Shadowing is nice to get a glimpse, and coursework and the MCAT get your mind in the right place, but honestly, until you work 2 triples and double running a total of 66 calls in a week, 24 of which were lights and sirens emergencies interacting with emergency room staff, it is tough to get an appriciation for the daily grind of the medical field.
I strongly recommend you do it. Honestly, I know that being an EMT is not the same as being a doctor, but neither is doing any research in a science lab. There is no place besides medical school to learn medical school information, so you might as well at least be doing something in the field. I take notes on interesting diagnosing, learn to fill out paperwork, and even read books and practice medical spanish.
As for companies not hiring for only 9 months, the EMT field is probably the best field to do it in. Everyone is short term. Most people are trying to get into medic school and are only there for 6 months to get their required 1000 hours. I work for a company with 70 employees, and no one has been working there for over a year. They will be cool with it