tl;dr - You probably want to either call the Washington Apple Care phone number or contact a Registered Broker / Navigator.
Long version:
With unusual circumstances like moving from out of state, I'd call the Washington exchange help phone number. They can probably explain what it takes to get coverage. My guess is that getting a new driver's license, signing a lease, showing a utilities connection receipt, or something like that would probably be enough. But that's just a guess.
I suspect you know this, but you should try to apply before the 15th of the month.
From the Washington State Special Enrollment Period checker: (
https://www.wahbexchange.org/wp-content/uploads/2020/06/SEP-Checker-2.pdf)
"Coverage start dates typically fall to the first of the month after selecting a plan. Some events automatically provide retroactive coverage, like birth. Coverage dates can begin later if you report coverage ending at a future date. You have 60 days to select a plan"
and
https://www.wahbexchange.org/new-customers/application-quick-tips/"Coverage Start Dates - If you want your coverage to begin next month, you must enroll by the 15th of the month. If you enroll after that, your coverage won’t start until the following month."
I'm not in Washington, but in my state the application process didn't take very long. I think I was able to apply and get approved the same day, but I don't remember. The difficulty I've had was that my state doesn't allow a letter describing unusual income situations as many other states do. My state required me to complete a form that was buried on their website. It took me weeks of looking and calling and getting my income projection rejected multiple times to finally find the form. For me that was by far the most difficult part.
If you're not able to apply until you have residency and you won't have residency until after the 15th, you can choose to rely on your ability to get COBRA and back-date the start date. With COBRA, you have 60 days to sign up and once you do your coverage start (on COBRA) is back-dated to when you left your job so you have no gap in coverage. I had that as a back-stop for my coverage when I FIREd. In your situation, how that could work is you could give notice on March 1, start your drive on March 15, and arrive around March 25 in Washington. Apply for coverage over the next ~20 days (before April 15) and your coverage on your Washington state plan would start May 1. You wouldn't be covered during the month of April, but if you suddenly had a need for coverage during that time you can sign up for COBRA before the end of April. You might have a day or two of no coverage because there are more than 60 days from March 1 through May 1 but that should be manageable. Just don't do anything stupid on April 30. :) If you take that route you could give someone you trust the information required to apply for COBRA in case you end up in a car crash during the drive and aren't able to complete the application.
The other option is that in some cases you can apply ahead of your eligibility date.
"Coverage dates can begin later if you report coverage ending at a future date. You have 60 days to select a plan. "
In that case you could apply during the first half of March even though you're not yet eligible. You might need to call the help phone number or work with either a Navigator or a Broker to find out if that's possible. You can be conditionally approved pending submission of additional documents. In that case you might need to apply during the first half of March and then get your Washington Driver's License right when you arrive. You could then submit a copy of your new license to prove residency, and your coverage should start at the beginning of April.
For the road trip, keep in mind that mid-March is often a very snowy time in parts of the Rockies. If you cross Colorado/Utah/Idaho/Wyoming during that time there's a decent chance you'll be driving through a blizzard on a mountain pass. I would only do that in a vehicle with good quality winter tires and then only if I really needed to. AWD doesn't help as much as good tires, so don't trust just being in an SUV to get through. If your schedule is flexible you could just plan to spend a few days in Denver/Salt Lake/Cheyenne/etc. if you run into bad weather. The good thing is that at that time of year there's generally enough sunshine to melt the snow within a day or two if one of those storms pass through so you probably wouldn't be delayed more than 1-2 days. The major interstates are also well maintained in those stated during winter, so once the weather clears the roads are clear pretty quickly.
And in that area there are often places without good cell phone coverage. I'd have plenty of music and/or podcasts downloaded if you're planning to use your phone for entertainment, and I'd also download some off-line googlemaps for that part of the drive as well.
