To dig out of the current state, treat it as two problems, because wet and sour is not only a carbon shortage.
It has gone anaerobic. The sour smell is what happens when there is no air, and adding carbon without adding air fixes half of it. So the actual repair is to turn it and mix carbon through as you go, not to layer cardboard on top. Empty it out if you can, and rebuild it mixing torn cardboard through every few forkfuls.
It is too wet. A pile should feel like a wrung-out sponge — damp, not dripping. If you squeeze a handful and water runs out, you need dry material and you need to keep rain off it. A lid or a sheet of something over an open bin makes a large difference in winter and costs nothing.
On ratios: the numbers people quote are for building a hot pile from scratch in one go. For a bin fed weekly, the useful version is by feel — if it smells sour, it wants more carbon and more air; if it is dry and nothing is happening, it wants more green and more water. That is the whole control loop and it is more reliable than measuring.
Winter also simply slows everything down. A cold pile in February that is damp and not smelling is fine and does not need rescuing; it will restart in spring. It is the smell you are fixing, not the speed.