Pusrchase on West Coast or Florida for cross country trip.

Might do a search through RVT.com to give you some idea of pricing for your dollars.

IDE say it's a toss up. I would buy in FL and do your cross country and west coast trip. Then see how quickly you could sell it in the Seattle area. Keep in mind if you try to sell quickly you are going to sell for a lot less than you paid for it. For the loss of money on a sale I would have it shipped back home.
The last thing you want to do is buy an RV mid trip and discover it has issues. That's why I would buy before your trip at home and use it in the area to figure out its quirks and if it will have issues.

Just curious, why are you not going to drive it up to Alaska?

I’d buy where you live to avoid registration and insurance issues.

As with a boat, plan on a break in period. I would lean towards florida if you can live on the boat for the first couple weeks while you get the motorhome sorted out and do a couple trial runs (if you find time consuming issue, you can live on the boat while the repair shop fixes it). Plus rather than buying all new stuff or shipping it across country, you can simply move it from the boat to the RV (bedding, cooking supplies, clothes, tools, etc...), at least that's what we always did when switching back and forth.

Are you planning to pull a car behind the MH? Unless you go really small, it's a pain to pack everything up when just going out for a day trip in the MH. Once you add the cost and complexity of pulling a car, look into picking up a similar size travel trailer or 5th wheel and truck as an alternative.

Arizona isn't a bad place to look but assuming a small to medium size Class C, it's not really a prime area (yes, you can find them). Snowbirds tend toward big units as they aren't moving a lot. Now if you are looking for a monster 5er and 1ton dually or a big diesel pusher MH, then it's a prime place to look.

I doubt you will save enough to worry about east coast vs west coast pricing.

I would look in southwest, AZ or NM or maybe in southern states.
I would not take a rig on the Alaska Highway without some sort of break-in time for you on the rig. Not many parts and repair places when you want them on highway.