Hey fellow pilot. I was a successful applicant this year and thought I would throw in my 2 cents. I didn't get as far as you in aviation; I was a flight instructor (CFI, CFII) for only 3 years before I decided to pursue medical school.
As a previous poster mentioned, adcomms will be interested in why you are switching from a career in aviation to a career in medicine. I was asked that at every interview. What they are particularly interested in is why you would give up a career where you could potentially make 6-figures, is relatively easier to succeed in (though actually being a pilot as well, I know that isn't completely true. As you know, in most cases it takes years upon years of flying the crappy legs before getting seniority and better pay!!), and you get to travel the world...for free.
Personally, I think it would be important to move completely away from aviation, especially if you know medicine is definitely for you. Based on my experiences stated above, there can be no question in the adcomms mind that you are committed 100%!! As an example, in my PS I stated, "having the opportunity to compare aviation and medicine first-hand, I knew without a doubt that flying was a great hobby, but not the career choice for me." If there is any doubt in the adcomms mind, they will merely say "next applicant."
However, I'm not sure EMT is the way to go. Perhaps consider an ER scribe or other type of scribe or technician position. To gain medical experience, I worked as an ophthalmic technician for several years. During those years, I worked VERY closely with several physicians, and as a result got over 5 extremely strong (or so they said) letters of recommendation. I was also able to see up close and personal all aspects of being a physician: from running a practice, to communicating with patients, to attending medical meetings, to dealing with insurance companies. In other words, I got to see the good, the bad and the very ugly of medicine. If you play your cards right, your application could be one of the most unique during the year you apply, ensuring that you very much stand out.
p.s. By all means, keep doing aviation as a hobby. Once you have the flying bug, it is forever; and as you stated, is meditative.
If you have any other questions, feel free to PM me.