There ya go, you just need to get a Stoeger!
It looks like you'll be spending a lot of $$ on shells. Buy a box of everything and shoot them, paying attention to the lot # on the box. In fact, when you buy the shells, check other boxes there to see if they have the same lot # on them. That way when you find one that shoots good in your gun you can go back to the store and buy a butt load of them and your problem will be solved.
Before someone says the lot # won't make a difference, I have solid evidence that it will, especially with the SST's.
Here's what I found for MY Tar-Hunt. I was trying different slugs and so was a buddy in his 11-87. I had 2 boxes of SST's (same lot #) that shot 1 1/2" group @ 100 and 4" group @ 200. That was the best grouping slug for my gun and my buddy found that the Remington's grouped the same as lightfields in his gun, with the Remington having a flatter trajectory.
Anyway, I had bought those at a Cabelas that is 1 1/4 hr. drive from the house. The local wally world had the same SST's (different lot) and was only 10 minutes away. So, I drove to Wally World and bought 2 more boxes. They shot like crap! 6" group @ 100 Yds. There was one more store that was somewhat close that had SST's as well, so I went there and bought 2 more boxes, different lot # than the others that I shot. Same results. So, I bit the bullet, and drove to Cabelas, taking the box flap with me to get the same lot #. I ended up purchasing a bunch of them, probably enough to last 10 years. They shot as good as teh first 2 boxes, so I'm set. What I heard was that Hornady has a couple of different loading machines, and one seems to give much better accuracy than the others.
With that said, I have never had any luck trying to get 3" 12 ga. magnum slugs to shoot.
Good luck! At least you won't be getting beat up with having a Lead Sled.