So, of course the P-clamp didn't work, as it was attaching the rack (which is already attached to the front wheel) to the head tube of the bike, which of course doesn't allow you to turn the handlebars. I shoulda seen that before I attached it.

BUT, I was able to get my hands on some Hanger Strap, bend it to the shape I needed, then double up with another piece and it works! I may put a 3rd or even 4th piece on later, but for now it's great and perfectly horizontal.