I read 'somewhere' that with the shotcup options available nowdays you can make any barrel shoot about any pattern you want, but it will cost you in time and material to make the right combination for your gun. As you state, you have a cyl. bore, so I would think that gives you kind of a head start on where you want to go and what will likely work; ie, tightening up patterns?, but you really need to know what pattern you are getting now with what loads. Have you tried a variety of factory brands and loads to see what they do now?
FWIW, my old 'Buck' barrel c/w sights is cyl. bored and it throws new shotcupped 12ga 7 1/2 or 6 loads out plenty good enough for me at 35-40yd., as is, for any practical use. Im only saving the full choked bird barrel for head shots at turkey, I think.