omg I don't mean to laugh - but I've had the same problem!
Jack, my Golden *loves* kitty snacks! I call them Kitty Roca (they look like almond roca - covered in litter)
I keep my cat boxes in the laundry room - and tried everything to keep him out of there! I ended up installing a cat door in the laundry room door - problem solved.
I know exactly what you mean about the cat poop breath - it could make you gag couldn't it! omg!!
I just trained Max right from the get-go to "NO!" "Stay!" right at the door. Now when I am in there doing laundry or scooping boxes or feeding the cats (I keep their bowl of dry food in that room too because Jack would scoff it down like he hadn't been fed in weeks!) and the door is opened, Max comes and lays down, with his paws just inches into the room
If he tries to creep forward all I have to say is "OUT!" and he backs up- it's pretty hillarious! I KNOW he'd snack in there too if he had the chance.
I love my dogs more than anything but - they are such gross and tasteless creatures sometimes!!
Good Luck Becki - that's a tough one to solve!
I'm sitting here laughing hysterically at the mental visual of the dog snacking as the cat extrudes - kind of like a kitty vending machine