IMO, Carroll, if you can convince him, makes the most sense. It's late in the recruiting process, we are a month away from programs shifting gears to spring workouts. If UW can convince him to leave his new job at the Seahawks, they should get him to be a placeholder for a year. He could keep whatever recruits you have left, I am sure he could put together a competent staff to recruit guys and he himself could recruit guys, and then this gives UW time to find a long term coach starting next year.
And since Pete would be giving up his future with the Seahawks in that front office role, maybe UW offers him something within their athletic department, which then can be sold to the players he goes out and recruits now, that he will remain around the program and maybe even have insight on who the next coach will be.