I understand your dilemma with the rat snakes. They will eat eggs and baby chicks but they are great to have around for rodent control. My general rule is that as long as they stay out of the coop I leave them alone. But if they go into the coop and start eating eggs they have to go. Luckily I have a friend that wants me to release them on her property. Since she wants me to that makes it legal and to me it's a lot better than killing them. I keep a snake stick, leather gloves, and a pillow case down there handy to catch one.
Snakes can come any time, day or night. With the pop door open thy can find a way inside. But they tend to prefer more protected way in and more often hunt at night. Can you seal other holes they are coming in and keep the area around the pop door cleared so they are exposed if they enter that way. They also like to use the same path into and out of the coop. If they are using something other than the pop door that's another reason to seal other holes.
I have not tried any commercial repellents for snakes, I have no idea what effect those might have on chickens. I've been pretty disappointed in the commercial and homemade repellents for deer, rabbit, and groundhogs but maybe you can find something that works.
If you want to trap them, you might try a minnow trap with pretty fine mesh. People say to bait them with eggs but I'm not sure how necessary that is. If you know where they are entering block the hole with the trap if you can. They should enter the trap trying to get in the coop.
Another method is to get some deer or bird netting and sort of wad that up near the entry point. The idea is that the snake gets tangled up in it and can't get way. I have not tried either of these traps but the principles seem solid. Of course when you catch it you have to do something with it.
I generally keep a golf ball in the nest as a fake egg. Several times I've had snakes ignore them, but a couple of times I had a snake swallow them and not be able to fit through the hole they came in. I don't know if the golf ball would eventually kill them by starving them to death, a snake can go a long time between meals. Or if it will eventually regurgitate the golf ball and live. I've read both. To eliminate the uncertainty I retrieved the golf balls with an ax.
I hope you can get something useful out of this. Good luck!
