Thanks, guys. I had ran them briefly through a clothes dryer before the first install, but they cooled quickly so I don't think it helped. I also was worried about melting the vinyl and only left them in for a couple of minutes. Someone suggested that approach on another thread, and I reckon it would have worked if I had heated them more.
Working with it in the sun made a big difference. I was amazed at how much more pliable it was. There were minimal wrinkles in the passenger seat cover, and they disappeared entirely while sitting in the sun, so I left them alone.