Close up

Your builder did a crap job there. Have him redo.

If you don't want to have builder redo, then what about "lining" the end sections like that with another material (like your stone) or paint over the wood.

Have him cut the boards back and use a vertical board/filler the same same thickness on each side with a miter

What about trying to case the opening? Would that be possible?

I think that is what @millworkman is suggesting.

Personally, I wouldn't want some workaround. You are having all that beautiful paneling right there at eye level. Not on the ceiling, not on the floor. You don't want casing to just detract from the effect.

Your contractor needs to "get it" right now, before going any further. He/She knows how to miter: get it done.

And yes, you can rip off the installed paneling. I'm not an expert, but I don't think that's a big deal. Just get it fixed.

How awful it must feel to have to tell an actual contractor how to do his/her job. I wouldn't want to be in your position. It looks awful as is.