When you consider that the price of a new 870, you have a decent deal on your hands. If you can pattern it -- do it. Shoot from 35 yards, with all chokes at least once. You should have about 60% on top, and 40% on bottom. Check for large holes. As far as getting it to shoot high (which it should if it is shooting properly), you can do a few things.
Put a mid bead on if there isn't already one. This way you can "aim" high more consistently.
Adjust the stock at the point where the butt-stock meets the receiver by loosening it (stock from the receiver) and placing shim at the top/bottom/left/right to make the gun shoot where you want it to. I suppose this is a bit like sighting in a rifle. But I hate to make metaphores between the two.
Play with your chokes and loads. Patterns have a lot to do with the chokes of course. But the load you are shooting does too. Reload a variety of loads and pattern them with the different chokes. Load different dram equiv., shot weights, different shot sizes, different wads, different hulls, and different primers. BUT FOLLOW THE RELOADING GUIDE TO THE DOT. Just load a bunch of different loads, and see what works best.
If I am picturing the proper gun you are speaking of -- they are beautiful. Good luck! Trap is fun, isn't it?
Hueco