I might look for a NCOWS group. I shot Cowboy Action Shooting back in the 1990s, and while the rules didn't allow high tech modifications, and you had to use period calibers, some people would use .38 Special because it had little recoil and they could shoot faster. Like a lot of these sports, it was all about speed, not accuracy. I had fun, and didn't complain in public, but to my friend that ran a lot of matches I did tell him why I didn't do it for more than a couple years. Every stage was "run...run...run!....shoot those 5 metal poppers about 10 yards in front of you with your pistol....run, run...run! Shoot that giant metal plate about 15 yards in front of you with the shotgun....run run run, shoot that big metal plate about 20 yards from you with your lever action. TIME! 30 seconds! You win! Most of the targets were so close you could teach a 10 year old who had never seen a gun, say from Mongolia, and he'd hit them all in 5 minutes. It was all about how fast you could work the trigger. If they would double or triple the ranges, it would be more of a sign of your marksmanship, instead of your cocking muscles.
I also shot BPCRS (blackpowder cartridge rifle silhouette) in those years. That sport was developed with strict rules to prevent an "arms race" that happens in most NRA sports. You shot at long ranges, slowly, with period single shot rifles and antique cartridges. You had to shoot well, or you didn't have a chance. You could buy at $5,000 custom engraved Shiloh Sharps if you wanted....but you had to be able to SHOOT it. Lots of poor guys did very well with old $200 Trapdoors and military rolling blocks. It was great, and the equalizer was one thing: can you shoot?
I've noticed the marksmanship competitions seem to be going away in my lifetime. Schutzen, bullseye, .22 matches, all are replaced by IPSC, Bowling Pin, SASS, Sporting Clays, and a lot of other "speed, quasi combat" type high tempo action. Which of course is more aggressive in action, and probably scares a lot of newbies away who think "I can't keep up with that guy! He just shot 15 rounds in 5 seconds, reloaded, and did it again!" Whereas the slow, relaxed target matches seemed calm and welcoming. My impression is Americans have gotten very "in your face" with our activities, and most are "extreme [fill in]". Maybe it's just me, there have been quickdraw competitions back in the 1950s, etc.