Never been near the Ozarks myself but we've had the exact same thing going on in Kent for years. Big black cats, multiple credible witnesses, the occasional mangled livestock that the authorities immediately chalk up to "a dog" or "natural causes." Classic deflection.
Three sightings in a month is significant though. Are we talking genuinely massive, like out-of-proportion-to-any-normal-cat massive? Because that's the key detail most people gloss over. Thier size estimate compared to nearby reference points tells you a lot about whether you're looking at a feral moggy having a good run or something that genuinely shouldn't be there.
The Ozarks terrain would suit a big predator perfectly, decent cover, plenty of deer. Honestly wouldn't surprise me at all if there's a breeding population that's been there for decades and the wildlife authorities simply don't want the headache of admitting it. Happens here constantly.
Keep a camera on you and try to get something in frame with it for scale next time. That's the only thing that shuts the sceptics up, temporarily at least.