Free: Contests & Raffles.
A little 400 grit sandpaper around the rough edges smooths it out
Rio and Federal Gold Medals are longest.Kent and Fiocchi are in the middle.Winchester is shortest.
I would also make sure your bolt is moving backward freely as if it is sticking/slow it might not be able to flick the open shell past the chamber opening. Also check that the extractor is in good shape.A big oops once... I had shells that would not eject all the way out of my 870 when I would fire one round and try to clear it into my hand, but when fired rapidly would shuck out with just a tiny amount of sticking. Turned out I had accidentally bought 3" shells the night before my duck hunting trip and I had a 2 3/4 slot in the side of the action. Luckily, I did not damage the gun or myself and traded shells with my buddy.
Good for you for trying, but by the time your done monkeying around with all the shell options, you could have replaced that shotgun with a Remington 870 or other model. Just speaking from experience. I picked up a similar one years ago for cheap and it lasted about a week, before someone else was a proud owner of it.
If you like shooting those 3 1/2" shells, I would consider an autoloader. I have a 3 1/2" Nova that has a long stroke to it.