Being that you are so new, I would rule out most of the remote areas (Nome, Barrow/North Slope, Dutch Harbor, etc). Not saying they would not hire you, however they look for more experienced and seasoned medics due to the austere environment. For example, my typical medevac flight lasted anywhere from 3-24 hours depending on weather. Take a critical patient whether trauma or medical and then manage them for that length of time. On the plus side, if you get in one of those areas, you will have some serious experience under your belt that most in the lower 48 will never see. I did my first field chest tube in Alaska, numerous surgical crics, hung blood, fibrinolytics, and delivered babies.
I recommend you look in Anchorage, Fairbanks, Juneau or Soldotna. You can get just an EMS job in the last 3, Anchorage is Fire-Rescue but they may be willing to train you since you will have MICP status. Juneau look for Capitol City EMS. Other possibilities but rare are in Ketchikan or Sitka. Keep in mind the majority of these areas have a heavy volunteer base and a lot of them simply have paid on call staff as well. If you want FT employment seek out the big 3 listed above.
If you can get in the North Slope, go for it! You will get lots of training and the pay is ok. When you see those $25-30/hour salaries do not forget the cost of living is HIGH. $6 for a gallon of milk is normal. Do not worry about housing as most of those remote places either have housing you can rent or some even provide it. It all comes down to negotiations when you interview, including moving costs, etc. Of course the city EMS or Fire services wont do that, just the remote areas.
In order to apply for a MICP you actually have to have an AK Medical Director already so that means you must get a job before you can apply. The departments know this and they work around it if they want you. Once you relocate, you get a provisional license but the MICP may take 4-8 weeks. I hate asking this, but have you visited Alaska? It is beautiful but a completely different way of life. It is a big jump if you are not as informed.
http://www.matsugov.us/admin/hr/jobopportunities
https://www.nortonsoundhealth.org/Join-NSHC/Vacancy-List
http://www.egovlink.com/ketchikan/postings.asp?listtype=JOB
http://www.cityofsitka.com/government/departments/fire/
http://www.juneau.org/ccfr/
http://www.cityofkotzebue.com/fire
http://www.north-slope.org/
This is a great resource
http://www.jobs.state.ak.us/
Also do not forget about USA JOBS as there are many military positions available in Alaska.