Honestly, theres not enough training at the emt level to warrant people paying to bring them over or house them. Most of the opportunities i see sre for paramedic or higher medical professions (nursing, midlevels, physician)
I see slots that become available for EMT-A's from time to time. Normally they are military contractor positions in Iraq and Afghanistan. The above is only one example, if you look around you may find more. I think its cheaper for them to hire EMT-A's and since many of the guys are prior service which is what they want. In terms of international disaster relief, that is hard to do even as a paramedic because there is such a large pool of higher level providers which often volunteer. Also many countries are more familiar with doctors and nurses than paramedics. Disaster response is really 99% logistics, HSE, public health ect. Of course local resources become overwhelmed but there is normally an over abundance of health care provider volunteers and not enough support, logistics, ect. At least from my experience. You can always ask "Doctors with out borders" though maybe they can point you in the right direction.