WOW. I have never seen mouthrot that bad before. Can't do a 100% diagnosis without a vet, but that's mouthrot if I've ever seen it. Going to be honest, I don't think this snake's chances are good at all, but you can still try. Hope you'll be keeping it during/after treatment, because it takes quite a bit of ignoring for something to get this bad.
Is he about to shed, or are the eyes infected as well? I've known some really bad mouth infections to cause eye infections (nothing you can do about that without a vet though). Take care of the mouth and the eyes will clear up afterward if that's the case though.
I've dealt with some fairly bad mouth infections before, so I'll try and modify what I've done for this case:
First off; QUARANTINE like crazy. This stuff is highly contagious so keep him away from other reptiles and don't use any equipment with him that you use for your others.
You're going to need to remove that gunk... I wouldn't use listerine, bc I don't think this snake can control whether or not it swallows something well. Plus, you want it to be able to drink. Use just a wet Q-tip and just get as much of that gunk as you can out. If the medication isn't touching anything but that goop it won't really do much good anyway. When you get it so that the snake can close it's mouth a bit better, then use the diluted betadine/hibiclens on the gum tissue. Get all/most of the gunk cleaned out in one go, then try treating it three or so times a day. When it starts looking better, you can decrease frequency. You're gonna need to keep cleaning his mouth WAY after things look fine to keep something like this from bouncing back.