Here is what I did to "break in" my 930:
Bring 15 rounds of 3" magnum slugs and a box of your Winchester 2 3/4" #4 birdshot
Shoot 5 3" slugs fast, slow, whatever you feel comfortable with. They try 5 shells of #4 and see if they all fire and extract without issue (as fast and as safely as you can or as your range allows). If you still get a malfunction, do another 5 slugs and repeat the cycle.
It took me one box of 5 3" magnum slugs before it would shoot cheap wally mart #4 birdshot.
Before that, I would have a few "stovepipes." After, all is good.
Cleaning is upto you, I clean my 930 three times per season and it's sitting in a case right now uncleaned since October

During my breakin session, I never cleaned it.
Hope that works for you!