PP membership exploded with the Citi Prestige card and then the Chase Sapphire Reserve card. I don't know how the PP-accepting lounges can handle it quite frankly. The DFW Club lounge has a waiting list for entry at times.
An alternate PP lounge is The Club lounges in A and S but they are quite a hike from Alaska gates. If you have a long layover, the lounge at A could be worth it. There is usually a ton of space and you can chalk up the hike to needed exercise