You need a permit to take the MSF course. If you want to get an AZ endorsement, you need an AZ permit. To get a permit in almost any state you need to take the written test. Most states, including AZ, will accept a MSF completion card in place of the driver's portion of the test.
I have both the beginner's and the experienced rider's courses. I was supposed to become an instructor last year, but I had to go on det. I am going to become one this year if I am back from det in time.
Honestly, the WA license is not a bad deal. It's cheap, it never expires while you're on active duty and it now doubles as a passport for travel to Canada. You can always swap back to AZ next time you go back if the "valid til 65" rule is that precious to ya.