So much fixing...
After I got all 7 rivnuts put in the inside back corner of each rear seat back, I went to get the plates that hold the bar across the back. Turns out that you can't install those small rectangular plates in either direction - they have to be the right way so the larger plates can be the right way.
I decided to add more rivnuts rather than to drill more holes in the large plate. I'm not 100% sure that was the right choice to make, but it seems to work. And, as always, it is a good reminder to plan the entire thing before drilling the first hole or pulling the first rivet.