Hi,
Thanks for the details. I have noticed some weird behaviour, as well as possible configuration issues:
1. There are other search plugins active as well, Search & Filter and the Pro version. I strongly recommend having only one search related plugin active.
2. When visiting the results page via URL, when the plugin override does not activate, there does not seem to be any pagination, for example: https://tvc.org/?s=well+chil
This leads me to think, that the results count on the results page might be set by the theme somewhere, to possibly a high number.
3. The other search bar on the bottom of the page seems to be working all right, the only difference I see is the override method. Can you please change that to GET on the header search as well? I’m almost sure it will resolve the issue.