There are 3 ranges that go to 200-600 down near Spanaway --Tacoma Sportsmen's Shooter's Club, Paul Bunyan and Ft. Lewis Range 15 (go in the back and you don't have to pass through post to reach the range complex --note NO OTHER rifle ranges there are for public use!). TSSC goes to 200 I think, Paul Bunyan goes past 200m (250-ish?) but opens to 600 for competitions. It's where many of the "for score" shoots are held. Range 15 is a 300m (or 300y?) range just before N. Gate, Ft. Lewis off Range Road. TSSC is a club, Paul Bunyan is a club and R15 is open to public and has discounts if you are military or a vet. First come, first serve and it used to get REALLY busy on weekends. I think it's open on Friday now and there weren't many people there when I drove by last week.
There is a shoot sponsored by someone further up where you are I think and they shoot steel past 1700m. But .50's still fuck up steel at that range, not even sure if they allow .338LM because some of the closer targets are at 600m. Most of those guys have wildcats or hot .30's, some 6.5's. Nothing beats shooting from one peak to another though, it puts a whole new spin on wind values. The prizes are usually pretty nice too and in the $600-ish range. There is a cost to participate and it lasts 2-3 days when they do it. This may be the FB club, don't know.
Tons of BLM land here, so I just go find an old clear cut somewhere and walk out a range and set it up. Be careful though, lots of hikers and dickheads that think they own it. Some dickhead shot a picture of a guy shooting a pistol in a clearcut and posted it online asking who it was --I couldn't figure out why. You have to go deep to get away from people sometimes though, just be careful. There are "spots" where people go shooting on BLM land, but I'd stay away from those unless you like wearing rifle plates and have a serious CLS kit --Bubba and the gang, you get it, if not then it's the place for you. I call one "ricochet range" because it's surrounded by stone and basically a 360 free fire.