I used to live in Olympia! So as far as the coop/run, if the current bedding is working in the coop and you're satisfied with it, keep using what you're using. I use wood chips in my coop (which goes into the run) but only plan on cleaning out and refilling it twice a year. I scoop out under the roost but that's the extent of regular cleaning for me.
Good to hear that the run isn't getting flooded since that can be a problem with fall and spring rains. I would recommend chunky aged wood chips (since you don't have time to age them I would look into undyed mulch, chunky as possible) as part of the run mix as they provide gaps for water to drain through. What I have right now is mostly wood chips with some remnants of dry grass and garden trimmings from summer, with dry-ish leaves on top - the chips allow rainwater to drain, the leaves provide a relatively drier mat on top for the chickens to walk on. Plus they love digging through all of it.
I literally have leaves spread out on my lawn to dry just so I can bag them and save the for later on in the year, sorted by leaf type. Anything that's too small (i.e. willow leaves) or soggy just gets tossed into the run. I want to get a pretty good layer of stuff built up before winter since I don't add anything through winter.
