I spent some more time coming up with an optimal route that visits every airport in WA. It just didn’t sit right that it was so easily to manually improve it. My code now first uses the LKH software which quickly gets a good starting point. Then it attempts to improve that route by moving, optionally reversing, sequences of up to 5 airports to other places in the route. Improvements are kept, and everything else is ignored. Doing this for 5 minutes gets me the route above, which required no manual tweaking, and is almost 100 miles shorter than the one from the previous post.
If there’s interest, I’ll see if I can turn this project into something useful to others.