I am curious: what are you planning on doing with the moss?

I make baskets and wreaths and plant them. I have them in my greenhouse where they are growing as I type. :)

Why not harvest as you use it? Then storage is not a problem....jjane

I want to store it and keep it green. After the rain stops we come to a distinct dry season and the moss dries up.

Do you know what kind of moss it is? Or can you image it and post it? Does it grow on the ground or on bark or on rocks-how is it growing?
I presume you are using the living moss to line the baskets
and wreaths.
From what you are saying I would think that you cannot store
the moss apart from its natural habitat without it dying. But you can grow it. Maybe you can grow it despite the fact that it is used to becoming dry. Some mosses will not do well without the season of dryness but for some going into
the dry cycle can be delayed by keeping the mosses watered.
Why don't you experiment. This should be no problem with the amount of moss that your area of the world produces.
Harvest some and let it dry out and then store it. Harvest some put into a pot without substrate but leave out where you can mist it daily to keep it fresh, and harvest some with the substrate and try to replicate the kind of substrate by mixing appropriate commercially available products, such as bark, peat moss, horticultural sand, coconut coif, etc. and plant your transplanted moss into it. Then tend it with daily misting seeing if it grows well.

But do try and find out what it is.
There is a site that features mosses of Seattle and I would
think that your species would be comparable.
Good luck.
By the way I do grow some NW mosses. The easiest is
Polystichum which is a tall moss that grows quite well in
pots and is a tall moss. I have an image of it but I would
have to email it to you if you wish to see it. Also I grow
a Leucobryon species and another clump type moss from Wisconsin. Plus others that I have not attempted to id out yet.
So to me growing is really the only solution to a fresh
green product.