Without a permanent resident card/valid visa, you won't be able to work in Alaska.
For pilot jobs, you won't be able to obtain a working visa.
For further ratings, you'll need a M1 visa as well.
I hope the two of you who have the green cards already know if they are still valid (outside the country for 6 months without a re-entry permit = invalid GC, just as an example...)

It's impossible to give further advice without knowing what immigration status you guys will have when entering the country.