Lee,
Keep in mind that you're talking a minimum of a 3 hour drive from Seward to Anchorage and approx 126 miles. I did a search for Seward's transportation and the only taxi I could find was just for the local area. (Some of the board's experts might have other alternatives) It looks like your options are the train, bus, or rental car. If you have enough time before your flight, it would be worth your while driving and viewing the unbelievable scenery!
Shar