First and foremost, what is your price range? What ranges are you going to be shooting? If your max distance is going to be 100 to 120 yds, then go with the rem 870 12 ga with a hastings barrel. Since it is a dedicated slug gun, get the barrel pinned and get a lighter sear spring to lighten the trigger. Some guys will push 150yds successfully with a 12 ga using the high velocity slugs. You definately need a fixed or pinned barrel for that. Reminigton makes the Rem 870 SPS SuperSlug with a fixed barrel and Ithica makes the Deerslayer III, but its around $1100, maybe more. If you want to try to take something 150 to 200 yds, go with the 20ga. The only problem is that if you refuse to get a bolt action, you probably need to spend about $1100 or more on a deerslayer III in 20 ga. I don't think a standard pump shotgun with a drop in barrel will be accurate enough at those ranges so you definately need a permanantly fixed barrel like the deerslayer III. If you did not have the issue with the bolt action shotguns, then you could get the savage 220 for around $500 more or less. I have heard guys saying tha they are getting sub moa groups with the savage 220.
The thing about shooting long range with slugs is that you need to spend allot of money on expensive slugs and shoot allot to know how your gun will perform at those distances. Not that you are but you can't be one of those guys who buys a rifle and a box of shells and uses half the box to sight it in and the other half to hunt with and assume you have a 200yd shooter.