You could use the SEA Hampton Inn. It's maybe 1/2 mile south of the DT on Pacific Hwy South, but on the other side of the street. The last time I checked their Park n Jet rate was $109 plus tax and included one night at the hotel plus 7 days of parking.
When I use this rate I book a regular rate online and then call the hotel directly to change it to a Park n Jet rate. You can't get this rate online. Also, they don't do PnJ stays from about May through September or October -- only during the winter. But you should be fine for March as long as they're not already booked up.
Their airport shuttle doesn't run on a regular schedule as the DT one does, but rather runs on demand 24 hours a day. Their breakfast starts earlier than the DT and the place is much more compact (which I like). On the other hand, the parking area has no attendant or gate as the DT does, so you may feel that your car is less protected in some way. I haven't had any problems though after a number of stays at the Hampton.