Throughout the entire DLC I've found .20 gauge shells. However, I
never found a single shotgun to use them with until I was actually in the Sierra Madre - I believe in the Executive Suites - which is within the last quarter to a third of the entire quest.
Did I completely overlook a shotgun placed in the Villa or somewhere else before entering the Sierra Madre.. or are you literally just stocking up on shells until you get to the Executive Suites?