I have lots of SXS shotguns as they are the only type I use. try some 1oz loads in your 12, you'll love the way it shoots and it will kill birds or targets no problem and easy on the shoulder. I have started using 3/4oz in 16's and 20's.
I only have one double rife a Heym 500 BPE with external hammers and a Jones underlever. it's a fun gun to shoot with 30gr of Trail Boss and a 365gr cast bullet.
When I shot trap, I would use 7/8 oz. for the first shot on doubles... 1 or 1 1/8 oz. on the second shot.. Those 7/8 oz. loads work great and barely kick. My son and I went to a fathers day trap shoot when he was 11, he used a 12ga. 870 loaded with 7/8 oz. loads. He walked away with prizes and $90.00 in cash. Good day for both father and son. You'd be surprised how well those light loads actually do, as long as they pattern well in you shotgun...