It has already been painted which means the paint normally has to come off to get new tile to sit over top. Do NOT wrap in real wood because this is a wood burning unit. You can use wood-look porcelain tiles (flooring tiles) to get this to work in that style.

Something has to happen to the painted surface to get anything else onto that surface. I'm hoping some tile guys will pop in to say hello and offer some advice.

I'm not sure if there is a primer out there that would work or if the paint has to be blasted off (sand blasted or some other form of physical removal). If you've never done tile before, then this is going to be a big DIY challenge.

Personally I would put the money away so that you can remove it at a later date.

I see nothing out of line with your style when it comes to the fireplace (which I really like) except the mirror. I could easily imagine a Victorian fretwork panel across the top of the mirror, roughly in the style of the one below, but in the wall colour. I think it would look gorgeous and be really rather boho.

https://za.pinterest.com/joorchids/fretwork/

This fireplace shouldn't interfere with your style--it's really a blank canvas. The mirror needs to go in favor of a a unique piece....possibly a framed scarf.

Play down the fireplace by adding a beautiful focal point. No wonder it doesn't look right. Take another look at your pictures. The mirror has to go. From one angle it reflects the ceiling and from the other it just looks like a black hole.

Your frustration with the fireplace seems misplaced.