Thank you @JamesStaddon and @laura-aome for your thoughts and ideas!
I’m keeping an eye out for materials that don’t wrinkle. A large curtain would be an option, Laura. The background I use now is a curtain. Most of the wrinkles are taken care of when I stretch the background with “A clamps”. I’ll have to try weighting down the bottom as well.
I tested the spray bottle method on a plan, wrinkly sheet. It didn’t work very well when that sheet was just hanging loose. I think I’d need to combine several methods. Have it not very wrinkly to start with, weigh it down, use a spray bottle, and stretch it tight.