Last year for our July 30th departure, we used Capital Aeroporter (apparently now called Premier Shuttle) for 4 adults and many bags. Efficient, prompt, clean transportation with excellent communication.
We pre-booked a private shuttle from SeaTac to the Fairmont Olympic for $115. Not exactly the cheapest option, but I highly recommend their service!
Seatac Premier SEA Airport Shuttle and Private Van Service | Seattle Airport Shuttle Taxi | Door to Door Shared Van Shuttle Express Service to Seattle (premierairportshuttle.com)