Blue Brick,
It sounds like there are two issues at work here, and they are very common issues with many shotguns, particularly the cheaper ones.
First, the chamber is probably rougher than it should be. This is likely due to the manufacturer not taking the time to sufficiently polish the chamber. Fortunately, you can do this yourself with an electric drill, a wire bore brush or chamber brush, and some 00 steel wool. Wrap the steel wool around the wire brush and chuck it into your drill. Apply a few drops of oil and polish at low/medium speed. It may take 10 to 15 minutes or so to adequately polish it.
Second, the Universal shells have a steel head. Steel heads have a tendency to stick to chambers much more than brass heads do, but they are cheaper to manufacture due to the cost of the material. You might try some other steel head shells since not all of them are created exactly the same. Or, better yet, switch to shells which have brass heads such as Winchester AA or Remington STS shells. These shells cost a little more than the Universals, but you usually get what you pay for.
To determine if the head is brass, just hold a magnet to the side of the head. If it is steel, the magnet will be attracted to it. If it is brass, the magnet won't be attracted to it. P.S. Don't hold the magnet to the primer area since all primers are attracted to magnets.
