OT: IF everything is right how is that going to hurt it? i guess being fat could wash but that wouldn't be right
some questions that hasn't been asked yet is what ratio do you mix your oil and what oil are you using? even being rich that plug looks more oil rich than anything.
how old is this snap-on gauge?
some other things to check on the carbs is the play in the slide. that brass pin can back out and wear. This can cause issues.
if you want to run with the lid off a easy way is to take a drill bit the size of a small screw you'll use and drill the plastic flang on each side of the top so it spins without biting. then take a smaller bit and drill the airbox(or run the screw in) so you have the right gap for the lid to fit on. when you bolt it on the top like this you can take the lid off and everything stays sealed.
there is a good sized radiator for a reason! if you want to putt in the woods pick up a quad more liking to this type of riding.