Skeet shooters in the 70's and 80's often shot a automatic for the 12 ga. event. Mid 70's were about the end of the three and four barrel sets as tube sets took over. A few tried to shoot 1100's in all four events, but by about 1980-1985 the tube set was king and barrel sets were dead as short barrels for Skeet.
The old SKB's used to have a case just like the one you have. Use to shoot with a fellow who had one. As I remember he shot the 28 about 90% of the time. Most of the late or current ones do seem to be the flat type. Am sure they both have been used. I guess it is fair to call a case perhaps 35-45 years old but old to me is nearer a hundred, pre-WWII at least. As to value it should fall in the $2-300 range. If you look on Ebay you will see cases like your form time to time sell in that range. Now to have one made today might set you back twice that much.