Thanks for your service to our country - it is deeply appreciated.
You need to obtain competent legal advice from both California and Washington in order to determine the proper course of action in your situation. I suggest that you do a Google search for attorneys Bruce Kapsack in San Francisco (who covers northern Cali) or James Bickford in San Diego (who covers southern Cali). For Washington, search Scott Wonder near Seattle. Any of these three will be able to give you all the guidance you'll need to get the right answers to your questions.
Best of luck during the remainder of your tour of duty and with your situation once you get home.
If you license was suspended as a reuslt of a criminal conviction in CA the WA will recognize that suspension and WA will not issue you a license unless you are eligible to receive a license in CA. Diana Lundin, with my office, is our Department of Licensing Guru. Feel free to contact her.