If someone breaks into your home, why are you maneuvering around your house ? That's just poor tactics.I prefer the remington 870 if going with a pistol grip style stock or any of the adapters that run an pistol grip. I put the large domed Wilson combat safety button on and find that i can easily de-activate the safety when placing my find on the trigger, the safety contacts the 1st part of my trigger finger by the knuckle and I can press it off. I prefer this over the tang safety of the mossberg 500 which requires reaching over the top of the gun, which is fine with a std stock but not optimum with a pistol grip. The maverick 88 which is very similar to a 500, although it has the safety mounted near the trigger which is impossible for me to reach with the trigger hand.
Better question is what will a HD shotgun do for you that a handgun will not? A pump gun will require 2 hands to run (unless you are Linda Hamilton) and be more difficult to maneuver through your house than a handgun. Mounting a light on a shotgun is doable but not as easy as a handgun. Accurate shot placement is king, and I would stake my worthless reputation on the fact that most will shoot a handgun more accurately than a shotgun. Reloads for HD are likely not needed, but a handgun will have a greater capacity and reloads are easier (not likely to carry a backup mag for your handgun in a HD scenario so that point may be moot) than a shotgun. And do you need a powerful shotgun for HD? if you are using mini shells or reduced power loads you may find something like 45acp or even 9mm is superior for the job at hand. A 45 acp pistol with a can sure seems like a better choice for HD...
There is a reason why gamers in video games hate 'campers'. It's because it's an effective strategy that is almost impossible to defeat.
Take up a defensive position with your shotgun, which provides an additional point of contact on your body for more accurate aiming, and wait for the intruder to come around the corner.
Then start putting holes in him big enough to put your fist in.
I am always amazed at how many people would give up a tactical advantage to go stalking an intruder. The idea is to win the gun fight. Not to be tacticool.