A friend repaired my kitchen popcorn ceiling with mud and used a broom (believe it or not) to kind of “swirl” and pockmark the mud. It’s not a perfect match to the rest of the texture, but pretty close. Screw it back to the beam, then mud & hope for the best. At worst you’ll have to have someone fix your fix, but at best, you’ll have saved a lot of money! As for paint…if the ceiling paint is old, it will not match the repaired spot, even if you use the exact same paint. I’m guessing you’ll have to repaint the whole ceiling.