As far as accuracy is concerned, a long barrel typicall improves accuracy. The shorter you get the less accurate the gun "should" become in theory. I would try a rifled choke as noted above. The "spinning" action the choke will put on the slug should set it straighter and therefore more accurate. 1 Foot low at only 50 yards seems a bit strange. In my opinion it should not be so much of a drop.

http://www.hr1871.com/Firearms/Shotguns/pardnerPump.asp they got a couple different ones ,ones a youth or small sized, its a 20 gauge but the stock may bolt to your recever. cool looking gun

my 870 remington had the same type of barrel bead sight.....takes some time to train your eye to keep the barrel level looking down the ramp to the bead...keep the gun on target untill the slug hits the target. I used to drop the gun after pulling the trigger that could make the slug go low...its like the same thing as shooting skeet and trap you can't stop after pulling the trigger follow thru the shot