About getting official status as a Wikimedia Foundation partner - the only requirement is to have three people agree to be a local contact. In other groups sometimes these local contacts have not been active Wikipedians, and the major responsibility is being dependable as a point of contact if something arises. For example, some organization in Seattle may contact a general Wikipedia forum asking for a referral, and the local group would be expected to at least refer them to whatever resources are at hand or tell them that no help is available.
There is an upcoming WikiConference in New York City next week. Several people from Seattle and Portland accepted scholarships to attend, and I will be asking them to meet each other and start the "user group" when they are here. If that sits for a while and we get a few more people interested, perhaps leading to having 8-12 Wikipedians regularly attending the monthly meetups in Seattle and Portland, then we could apply for community organizer funds especially if we can get a partner organization to also match the funding and do staff supervision. If it comes to pass that other people in the region would benefit from
having travel expenses and hostel lodging funded to attend Wikimedia
events then that is available for people who regularly contribute to
Wikimedia projects, and meeting other people in person does make for
more efficient partnerships.
Something else about getting official chapter status - in the last month our own Cindy (user:Cindamuse) from Kennewick had just joined the Wikimedia Affiliations committee, which is the group that issues official recognition to local community groups and grants them licenses to use the Wikipedia/Wikimedia names and logos. She would have continued to be an awesome supporter and organizer for us but on the night she arrived at a conference she met the other Wikipedians there then died in the night unexpectedly of a long-standing health problem. Cindy had wanted Wikipedia outreach to the major universities in the area and women's engagement programs developed. It is a horrible loss for our family and a big loss for our regional Wikimedia community, but it does show that some people had been planning what you propose, Pine.
In the example you gave, we might be able to ask the Gates Foundation to hire a Wikipedia community organizer to help manage local events and coordinate projects with research organizations in the area and beyond. Here is the grant request which led to the Wikimedia Foundation paying Consumer Reports, who after the grant period have kept me as their Wikipedian.
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https://meta.wikimedia.org/wiki/Grants:PEG/Consumer_Reports/Wikipedian_in_Residence>
I pitched Gates Foundation staff many times when I was in Seattle and a bit over the last couple of years. Things have changed since then, but I still think it would be in their interest to promote Wikipedia. For anyone who wants to get an in to the confluence where biomedical research meets the public, there are lots of opportunities in Seattle to attend public presentations by any organization one can find, but I might recommend attending this June 3 meetup by Northwest Association of Biomedical Researchers.