With you on that. I dropped my NRA membership in 1994 after being a member for 20 years. Even then I was just fed up with the approach of its management and what I viewed as its increasing failure to provide the services to, and representation of, its members in ways that it claimed. Will rejoin when they straighten out their leadership mess. It is good to see alternative organizations developing. But for my own part, I won't even join a local club so long as it requires NRA membership, and their stranglehold on this and the approach they take is another example of their managerial approach. Just a personal choice I feel I have to live with. Sad, but that's the way I feel I have to go. Not even trying to convince anyone else.
The relatively small club I shoot my BP rifles at (as a non-member, since it requires NRA membership to join) offers monthly matches as well in High Power Rifle. I suspect this may be more prevalent than you think. Well, I hope, anyway. I can't shoot in those any longer since I can't "assume the position" as a result of prior skeletal damage.