When you say "door height," do you mean that you want to store it in an enclosed storage facility? ...or one outdoors but covered?
There are plenty of "covered" RV storage facilities located inside many of the self-storage places in the area (
like these) that are covered but not completely enclosed.
If you choose a place outside of Seattle itself, you'll find better rates. Out in the suburbs or further will find better values.
One place we recommend to people to check is Nor'West in North Bend. It's a nice but small RV park that also has covered storage (their small complex also has a nicely kept mobile home park and short-term apartments). It's a very well-maintained and clean facility. It's just a few miles from the mountains and also very convenient to Seattle as it's right along I-90 (even though it's close to the freeway, the RV park itself is pretty insulated from the noise ...or so we've experienced but that shouldn't concern you for storage only).
Take a look at
THIS SLIDE SHOW that gives photos of their their covered storage facilities.
Nor'West website --
go HERE
Another covered RV storage facility that others have recommended to us in the past is Eagle Self Storage in Woodinville ...an image of their covered RV storage area --
go HERE (as you can see, they have plenty of height)
Eagle Self Storage website --
go HERE
These are just two places but there are dozens more like these in the area. PM me if you need help.