I don't like the rod idea. You need a custom steel frame that attaches to at least 2 wall studs and supports the bottom of the slab. Paint it flat black, keep it 6" away from the edges, and it will nearly disappear.

Sochi did a live edge walnut vanity several years ago. It's hard to tell exactly what she did from the photos, and it looks like her slab might be longer than you're talking about (maybe), but you might try contacting her via this site and asking. I've seen her commenting on the Home Decorating Site recently. Here's a link to her bathroom reveal: sochi's beautiful bathroom

If you're afraid to stand on it after it's installed, it ain't right.