If you wanted to go deep into the rabbit hole with a centerfire you could do a 6mmPPC benchrest rifle. There are a lot of really awesome used ones out there like on Benchrest sites.
My favorite old man story of grave disappointment was 38 years ago, back when prairie dog shooting at medium distances was my focus of activity.
I was out of town and decided to go to the gun stores there for the fun of it. I see a wild looking target rifle displayed. Turned out a guy soon to pass on was selling all his stuff and had put his winning 6mmPPC bench rifle on consignment. A sleeved 40x action, heavy match barrel, 2oz trigger, fancy BR stock, dies, brass, bullets, load data, and not a few groups at 200Y in the .3's as well as 100Y groups half that. It was $600 back then which was the worth what most of my regular guns were at the time.
I wish I could say I bought it but I went home, thought about it, decided I'd buy it, so I called, and it was gone already.
After that literally two decades past of buying a bunch of stock rifles that rarely even shot MOA. Talk about a waste of money and time and because I had to trade in or put stuff on consignment. If only..... I'll say this though, I learned what I didn't like, LOL!
You know what I did then 20 years later now that I had some money as a respite?? I went down to Phoenix during a BR match, found a good deal on used custom action 6mmPPC, which had a sliding extractor capable of taking a .470 bolt face, and drove away with it. Yes it even came with dies, brass, etc. Went out a few days later to shoot it, and the worst group was 1/2" at 100Y. .3" was seemingly easy.
With that rifle, months later, at sunup on a very calm morning, I was able to hit my MGM mini popper quite often at 1000Y!
I began to learn about BC's and long range so I had that gun built to 6.5-284. Later that year I got high score by a large margin at our local annual 1000Y match with it.
Lester Bruno around this time period, who is a champion short range BR shooter, brought his 6mmPPC BR rifle to a 300Y F-class match, won it and his group wasn't much over an inch. He told me he used his old worn brass, his left over bullets, and leftover powder, just to use them up.
I think a 6mmBR, or wildcat of, would do pretty much the same thing?? But the problem is you have to shoot at "REALLY" small stuff, or groups on paper, or you get too bored inside 400Y.
Which brings it all back to pcp air rifles, ELR distances for such a gun, and having some challenge in the wind, without having to pay the idiotic prices of 22rf match ammo these days or the other components for centerfire.