Having just read thru this post, I see you have the basics and seem to have checked most of them.
First off, 6" is NOT the norm. Like a couple guys here I have many many handis and NONE OF THEM is that bad!! SOME started close thou!! LOL Even my 500 that like to throw flyer's keeps its shots with in 3-4" at 100.
OK, you have a good mount that has been checked, same for the rings. That's a good name brand scope, but was it new to you? One thing many people just assume is that something new must be OK. Even with the top shelf stuff, things happen occasionally. Has it been on a different firearm that DID shot well?
How the rifle shot is huge with a handi. As mentioned the front rest should be as close to the hinge as possible and the trigger pull consistent and fully to the rear. Then just closing the action needs to be consistent and firm. As Tim mentioned, check and clean the latch and barrel shelf. Maybe even check the engagement as even doing all I just suggested, if that engagement is not even. Say only touching on one side, it cannot possible latch the same everytime. this will most definitely cause errant shots and loose groups. Check and adjust the forend, a "O"O ring or nylon.poly washer is a quick and easy way to float the forend. Also make sure that that forend is not too tite. This is a subjective thing but it shouldn't be stiff removing or installing. But shouldn't just fall off/on either.
Polishing the bore is way down i the list of accuracy alterations for me. Yes it will effect things, but generally this is more of a fine tuning alteration.
All this is outlined in depth in the FAQ's.
Good luck and MERRY CHRISTMAS!!
CW