My guess is that the seminary is being ran by Fr. Ercoli and Fr. Hector Romero. They are in Seattle.
I have to wonder how they ended up having a seminary there knowing the group. They don't even have missions west of the Mississippi, if I remember correctly.
The author of the first quote does present a plausible explanation, though it still seems odd. Bishop Dolan, and one presumes now Bishop McGuire, had a relationship (it perhaps wouldn't be considered as being a "mission", but IDK) with Our Lady of Guadalupe in Spokane, first Fr. Kevin Vallencourt (sp?)) and now a Fr. Gerald Kasik, and Holy Redeemer Chapel in Seattle, with Fr. Carlos Ercoli and Fr. Hector Romero. Holy Redeemer also established St. Joseph's Chapel in Mount Vernon, WA. I believe they acquired a small mission chapel that the Archdiocese of Seattle had closed. Bishop Dolan would go to these chapels for Confirmation, and I presume he supplied their Holy Oils.
When Bishop Dolan removed seminarians from Most Holy Trinity (Bishop Sanborn) perhaps they went to stay with Fathers Ercoli and Romero in Seattle. What would seem surprising about doing that is housing costs in Seattle are high (perhaps there is a very large rectory at Holy Redeemer?), it's not centrally located, there are only two priests, and a bustling urban area doesn't seem best suited for priestly formation. On the other hand West Chester, Ohio is more centrally located, has five priests in residence (per the SGG bulletin), and rent appears to be lower than in Seattle. Perhaps the "seminary" is actually at the Mount Vernon Chapel but Bishop McGuire said Seattle because few outside of Washington (and British Columbia) would know where Mount Vernon and the Skagit Valley are. Mount Vernon would be a great location (quiet, rural) for a seminary, and there are three Amtrak trains a day through there, with a connection in Everett or Seattle to the Empire Builder through to Chicago and points in between.