How long is your barrel and what kind of choke do you have now? I don't have a separate slug barrel on my Model 11, but I get reasonable accuracy out to about 50 yards by shooting 2 3/4 inch Remington Sluggers (rifled slugs) through my 26 inch Improved Cylinder barrel. I use only a bead front sight. I don't think rifled slugs are any more accurate out of a Cylinder barrel than they are out of an IC barrel either. However, I'd be afraid to try shooting rifled slugs out of any tighter choke constriction than an IC barrel.
If what you're talking about is getting a RIFLED shotgun barrel, so you can shoot SABOTED slugs that's a different kettle of fish. You'd probably have at least a 100 yard effective range with that; if there was such a barrel, but I'm not sure there is. I've never heard of a rifled barrel for a Model 11.
If your problem is just that your gun is too tightly choked (constricted ) to even shoot rifled slugs, a full service gunsmith could probably cut your barrel down by 3" or so and install fixed sights. I don't know if that would remove enough barrel to completely eliminate the choke constriction, but I think it probably would. You could still shoot shotshells through it too. You'd just have a 3" shorter barrel which would probably be close to being a cylinder barrel. The gunsmith could tell you for sure how much this would open up your barrel. Of course it might cost more to do all this than its worth. Can't help you there.
PS to Logs: Cracked stocks can be replaced. Try Bob's Gun Shop in Arkansas (You can Google it.)