A professional drain cleaner's snake with a properly sized cutting head will ream out the pipe to the original size...a typical homeowner's snake head is usually not that large and just pokes holes in obstructions. Because of the significant torque, a big head when it meets an obstruction, can generate some huge forces, and is best left to a pro to use. The snake can twist and break bones, lacerate fingers, tear things off, etc, when not used by someone with experience (and even then, if they have a lapse!). An AAV, should you add one where you already have an atmospheric vent, is a waste. Plus, it must be left accessible for replacement, since they do fail eventually.