Washington Rifle & Pistol Association website is here: WA STATE RIFLE & PISTOL ASSOC
Some searching with Google should get you some contacts for Idaho, Oregon, Montana, etc. You want the High Power Rifle program coordinator/director/chair person, fwiw.
I can't speak with absolute certainty for some of the other ranges in Oregon, or the ones in Idaho or Montana... but at the one civilian long range facility in Washington, Rattlesnake Mountain (TRI-CITIES SHOOTING ASSOCIATION (TCSA)
) or Douglas Ridge near Portland Oregon (Douglas Ridge Rifle Club
), Any Rifle / Any Sight (commonly referred to as 'Any/Any') shooting tends to be fairly small. Typically there will be a Palma match - 2 sighting shots + 15 shots for record at 800, 900, & 1000yds each - and then another stage usually consisting of unlimited sighters, 20 shots for record, with a time limit of 30 minutes, @ 1000yds. Some events may run it as 'Any Rifle Iron Sights' one day, and Any/Any the next day. Other ranges/states may run 3x1000yd events and may be more open to Any/Any than around here.
There are a few shooters who shoot Any/Any all the way through, though. They kind of fall between the cracks - they don't quite fit in the iron-sight/sling category, and they don't fit in the F-Class category either (they could, but I've yet to see anyone willingly choose to shoot on the F-Class target with a sling and have pretentions of winning). Typically if there aren't at least five shooters in a particular class, there are no awards, etc. for that group if it can't be rolled up into the next higher class/category.
Sometimes I see a few shooters shooting Any/Any for Mid-Range Prone matches (300, 500, or 600yds) - but most of 'em are the same few who shoot Any/Any at LR events because they refuse to give up the sling, but cannot properly utilize iron sights due to vision problems.
Just to be clear, I'm not necessarily trying to discourage you from shooting Any/Any, but I do want to make it clear that at some ranges at least, you'd be the exception to the rule if you showed up to shoot Any/Any all the way thru, and the odds of there being any awards available regardless of how well you shoot may be vanishingly small.
If you are still interested in trying out Any/Any - or even regular iron sights ala Palma - let me know. Its entirely possible I might be able to bring an extra rifle + ammo to an event later this fall @ Rattlesnake, if you don't find something closer to you.
As an aside... if you are looking for something a little closer to 'hunting rifle' application... have you considered F-Class?