The cat seems to like it...
I ended up spray painting the mirror (Craigs List, $30), but in retrospect I think I should have used a brush. I may still do that, so I can get a color that matches the towel better. Because of all the grooves and ornateness of the mirror, I think a brush would work fine on it and not leave those despised brush strokes visible.these:
Etsy, but it was the wrong size and slightly wrong colors for what I wanted. So I recreated it, and I hope that's okay. I won't be selling it or anything. Painted this $2 gilded frame white to match the trim and cabinets. For that I did use a brush and it came out great.
Painting the cabinets turned out to be quite a pain. I think I didn't sand them sufficiently. So when I did the first door with a nice brush, and still saw too much brush strokage and uneven coverage, I had to sand them down again. I opted to use an electrical sander this time, and the paint all started beading up in a few places and creating edges and it was just a mess.
But I finally prevailed and got the whole thing painted using a small foam roller. That required a lot of coats of paint, but looks so much smoother and professionally finished. For me, definitely the way to go.
Taping the walls (and then retaping for the second color) took some time, but it was worth it. And I didn't have to do very much touch up. I did use a level, if you are wondering.
I think I will probably go with this rug from Garnet Hill, and be done with it all! Hopefully it actually looks like the internet photo.