You can definitely find a horizontal mirror to lean on the mantle, resting on the wall. Another idea is "layering" framed artwork leaning up against the wall to cover up the opening. I have also done combinations of books and other items to cover areas above a mantle that I've wanted to cover. You can google all kinds of images (leaning mirrors and artwork on mantles). You can also add other interesting and lovely pieces in front of the mirror on the mantle. Good idea!

Mirror the wall, then hang a painting on the mirror (with Scotch strips).

I would suggest a different approach w/ 2 variations. I'm not big fan of mirrors over mantels. I know they're supposed to make room look bigger, but not my thing. And they're terribly commonplace, almost predictable. I would frame the overmantel area by extending the pedestals outside the surround to soffit. Then, one, you could install narrower matching horizontal wood pieces above mantel, covering cut-out, & just under soffit. Then hang a painting inside the overmantel frame. Or two, instead of horizontal frame pieces, cover space betw. vertical pieces w/ beadboard or hardwood veneered plywood, then hang painting. These could be attached so they could removed w/o causing lots of damage, preserving the eqmt. cut-out. Attached is a pic of my oak veneered plywood I used. Other hardwood options are available. Tomorrow I could to PS example if you like.

Interesting idea to extend the fireplace sides up to ceiling trim. But, that would be a lot of work. Just drywall over the opening for the cable box and choose a wonderful piece of art or a group of artworks to hang above the mantel. You could, in the alternative, group some objects of varying heights on the mantel but it's a pretty large space and objects could look too small. You might consider painting that space a color different from the room's walls. But, my first choice would be art.

Chipsbird, actually the design of the pedestals is simple, & there'd be no sophisticated joinery req'd, so it would be pretty simple. I make no claims to being an artisan or master craftsman, but I've done projects more involved than my suggestion would be. One reason is it'd be painted, making it easier to cover mistakes. Ellen's won't have shelves like mine above, so fabrication pretty simple.

Couple PS mock-ups, one w/ overmantel framed on all 4 sides & another framed only on 2 sides w/ beadboard insert.