Fast-forward a few weeks and I'm super happy how it turned out.
I ended up making a bracket so the reel would sit the way I wanted it. I used 3/16" plate steel, since that's what the reel had. (Clearly overkill for the bracket in hindsight.) I 3D printed a drill jig to get the holes to line up exactly with the brackets on the lift and reel, then practiced my TIG welding make up the bracket. I got a can of PPG paint in a catalyzed can (MaxSpray) at my local auto paint shop. The color is an off-the-shelf PPG color, but you really have to study it to notice they are not quite identical. I wanted to used catalyzed paint so I wouldn't have problems with solvents ruining regular spray paint. Have to say, when it was all done, it looks like a factory option to me. Just thought I'd share in case it inspires anyone....
