There is no texture under the hardwood. I scraped it off.

One good thing about where the hardwood is now, is that it's across the front of the fireplace. So, I can just leave it there, and maybe mount some small spotlights on it, or something.
As far as mounting the screen in the new place; I did get some advice from another forum. They suggested I use some sort of heavy duty shelf brackets. I'm considering doing just that. They won't look as good as the hardwood. But, the advantage would be that they're easy to install, and later move (if I change my mind again), without a lot of work, and damage.