Always an option to crack the market is volunteering first in the 3rd world, esp places like Africa.Then use that to network and get experience moving into paid contract work. Working in Africa there is usually an Ex-pat network of volunteers, UN contractors, mercs, scientists, mining groups you will quickly get in with at some local bar or meeting place. I've known guys go there as med volunteers and end up scoring gigs as Transport managers and project leaders on big dollars for major Euro companies in the first 6 months lol! Its not always what qualifications you have that count in the 3rd world, just what you can do, and who you meet. Then you can contract forever once you have that on the CV.
I'd suggest googling St johns ambulance in any african country/city or their local private EMS per country. There are 50 countries in Africa, over a billion people, and the EMS vary from non existant to quite modern ambulance services for the better areas of the major cities.
In between you can find opportunities even for unskilled volunteer assistance, and certainly a lot will be happy to have a person with the US EMT-B. Some of them are happy to have a first aider just to teach first aid to people in the community. (Some of these places will train paramedics to perform appendacectomies due to severe shortages, under direction of a doctor!)
I lined up contacts to volunteer at large hospitals in Uganda, Nigeria and Zimbabwe and also Indonesia within a couple of weeks of emailing. The hardest was getting people to answer the emails as developing country time runs different from our ideas of quick service.
There are also groups like MSF and orderofmalta.org , order of St Lazarus you can register with as a volunteer too. Some want a lot of money to join, some want nothing. A lot of the time if you contact a hospital or EMS yourself directly they may house and feed you.Also remember 1 USD goes a long way there. Just make sure you have some backup funds to leave when you want and good travel insurance.
