How I've solved (most) nap time issues.
1. Only enroll infants. Start the nap time good behavior early!
2. I bought some pirate treasure sticker "maps" and a treasure box which I fill with novelty toys like squishies, noise putty, mini playdough, mini slinkies, water tattoos etc. Each kid over the age of two has the opportunity to earn two stickers per day. One for no timeouts and another for "not being disruptive" during nap time. When they fill their map they get to pick a treasure. I frequently let them know if they are "risking" a sticker. I learned not to let them put stickers on or pick from the treasure chest when their parents are present. Power struggle
I was amazed at how well this worked for behavior issues!!! Peer pressure, bribery, and positive reinforcement.
I can't say the treasure box will stop the bad habit but maybe! I actually started it because of a bad napper and it worked instantly for her (2yo). I have sat and literally stared blank faced at disruptive nappers before. The trick is zero expression. They don't know what to think but it usually works and they don't much want you to keep doing it every day.