Actually the 336 is easy to clean from the breech. Cock the half way open take the screw out that holds the lever in,now slide the lever down and out,grab the rear of the bolt & pull it out.There's a small part on the left side if the reciever {the ejector clip}it just sits in the reciever,take it out so it dont get lost.Clean your rifle from the breech.When your replace the ejector clip,slide the bolt half way in install the lever and replace the lever screw.

This is alot easier to do than it is to explain.Or you could just buy an Otis cleaning kit.