Norwegian here so I've never been to the Ozarks, but screaming sounds at night that aren't a fox is basically my whole neighbourhood in autumn lol. We've got lynx out here and honestly the first time I heard one I was ready to call the police.
Genuinely curious what you're ruling out though - fox, rabbit in distress, barn owl? Because all three of those will ruin your sleep and make you think something is dying horribly nearby. I got into paranormal photography partly because I kept hearing stuff at night and wanted to actually document it rather than just stand there panicking with a torch.
Has anyone managed to record it? That would narrow things down massively. Even a shaky phone clip would help.