I think the Sportsman 48s are similar to the Auto-5, and the internet myth about Auto-5s not functioning properly with short barrels is just that, a MYTH. Aside from just not being the case in the real world, it's nonsense when you think about it.
There is about 50+ pounds of spring pressure pushing against the barrel recoil of an Auto-5 (my scales say 53.5# on the circa 1954 spring). A fired round has to overcome this 50+ pounds of force plus the inertia weight of the barrel. 12" of barrel weighs about 8 ounces or so. Reducing the weight of the barrel by 8 ounces, which is rather insignificant compared to the additional 50 pounds of spring force, isn't going to matter. Furthermore, LESS weight in the barrel will just make the recoil MORE likely to cycle the action, not less likely.