Try Puget Ridge Co-housing.
http://www.cohousing.org/directory/view/2954
If they can’t accommodate you, they will probably have some leads for you.
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Also try:
St. James Lutheran Church
9421 18th Ave. S.W.
Seattle, WA 98106
Phone: 206-767-5940
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Here’s another resource for Community Kitchens in the area. Unfortunately, they don’t have any kitchens right here in West Seattle, but they can probably give you more ideas.
http://www.communitykitchensnw.org/cook-with-us/