Shoot light loads or maybe have a competent gunsmith port your barrel. That will help with muzzle rise. If you had a Remington 870 or Mossberg 500 I would say look into the Knoxx stock. Sorry I forget the actual name of it, but lots of shotgunners say it's great.
I agree with Maser. I own a Win. 1300 & Rem 870. You can reduced recoil a lot of ways. For example, the reduced recoil ammo really works, but not for use in every situation. You can add a limbsaver pad. If synthetic it just screws on, or you can use the slip on variety. You can fill the stock with some lead weights or buy the mercury type recoil reducers. Anything that spreads the peak recoil will help.
In my opinion you can (in order):
1) Shoot a lighter load
2) Buy a semi-automatic (not worth doing but, sorry, just had to say it.)
3) Add a stock-pad recoil absorbing device)
4) Add weight to the gun (a mercury reducer in the stock and on the end of the magazine; pay attention to the gun's balance)
5) Change the stock to make the gun fit you better (A whole discussion in itself)
5a) Alter the stock to add gun flip which will reduce felt recoil and create other problems.
6) Add a "regular" recoil pad
7) Lengthen the forcing cone
8) Port the barrel (I suggest that this adds to felt recoil but reduces bbl flip)
I would just add low cost way that worked for me on my synthetic 1300. I filled the hollow stock with Styrofoam, then about mid-way I inserted a package of lead weights, then more Styrofoam and a the end another package of lead weights. Of course the weight in itself helps, but I feel having the weights float acts similar to the mercury reducers. Then finished with a limbsaver pad.
there have been several options mentioned.
Some did not list the drawbacks.
Knoxs stocks are pistol/shoulder style and change the feel.(except the comp stock which reduces recoil less than Spec-ops stock.)
Lenghten forcing cone and backboring are expensive.
mercury suppesors and lead add weight.
Reduced power loads have less pellets, less energy or both.(I don't think most targets will notice the difference.
I would suggest pratice with light loads and stoke it up for hd.
just use the right load for the job. for example there is no need to shoot 1 1/4oz loads to bust clays, 1oz does fine. things like that, no need for overkill. next i'd suggest an Xcoil recoil pad, i got one fit and finish is good and didn tcost that much, works well. super easy install.