When I had a 12 ga. SxS like yours, I used felt OP wads made of this material
http://www.durofelt.com/image_26.html I cut my own wads with a punch made by one of our members who goes by the name of Ohio Ramrod on this forum. He will make you a custom punch cheaper than you can buy one anywhere else. The OP wad needs to be tight and can be contrary to get through a full choke but it will go and it is easy to straighten up and seat properly as you press it down with your rammer. I liked to lube mine with just a bit of Bore Butter. I would lightly butter a piece of the felt like buttering toast and then put it in the microwave just long enough to melt the Bore Butter into the felt. When it cools, I would use my punch to punch out my OP wads. The felt should be just slightly lubed, not juicy. Not nearly enough lube to foul your powder. I used commercial OS cards. If I were using a light charge, one OS card was enough but if I were using a heavy charge, I would use 2 OS cards jut to make sure that the charge in the unfired barrel did not move forward when the other barrel was fired.
Pattern your loads to see which one gives you the best pattern. If you are finding doughnut holes in your pattern, this is usually caused by the OP wad going through your shot column. I have found that if this happens, as it did with one of my smoothbore fowlers, I just started using fiber wads and would separate them into two or three pieces before loading. By doing this, they did their job inside the bore but upon exiting the muzzle, they flew apart and quickly lost velocity and dropped away behind the shot column.
I had one fowler that gave me problems with the shot pattern having holes in it. It would scatter the shot and give a poor pattern. A good friend gave me this tip. Make paper shot cups to encase the shot in the bore. It is simple thing to do and works quite well as a way to tighten your pattern. Another advantage to the paper shot cups is that you can use a tiny dab of glue to stick your OP wad to the center of the paper cup. Upon exiting the muzzle, the petals of the shot cup open and act as a parachute to very quickly slow the OP wad and keep it from going through your shot column. If you are interested, give me a PM and I will explain how to make and use the paper shot cups.