As hard as I try to not "give away" pieces in a game by checking the square that I am moving to first, paying special attention to the "long range" pieces of my opponent, and calculating exchanges, I can't seem to stop blowing a won game by hanging a piece or two. Bishops seem to give me the most trouble as they just seem to blend in the background late in the game for me, and then just snap off a piece of mine as I think I'm close to giving checkmate. Especially late in the game I just seem to get "tunnel vision" with what I'm doing and the lapse in concentration costs me a piece and the game. Will power doesn't seem to be doing it for me, so what else can I do to stop hanging pieces??
You speak the language of my people.
There's nothing magical, unfortunately. You must avoid 'target fixation'. That is, even if you're close to delivering mate, you have to stop before every move, and look at every piece your opponent has. Every time. And you must remember that your opponent is choosing moves for a reason. One of those reasons is to snap your pieces off the board.
So the other thing you can do is to be cognizant of basic tactics such as pins, forks, x-rays, etc. You can work on these by running a tactics trainer.
I have the same problem with the bishops, probably because they are long range pieces and also because they tend to blend in with the pawns. The old advice was to sit on your hands and not move too quickly. Examine all your opponent's potential attacks first. Another suggestion was to write your move down before making it and then check the board again one more time. This problem should diminish with experience, but unfortunately it never seems to go away completely and all you can do is try to keep it to a minimum. Even GM's have occasionally overlooked a simple attack.
To be honest it is a little like spacial awareness. When I started playing I like most others left pieces hanging but over time I kind got used to "knowing" if something was en prise or not, most of my thinking is now strategic only doing concrete calculation when it feels necessary. I know I am being slightly vague but I would suggest honing your spacial skills by playing as much as possible, reading through annotated games by strong players and solving chess puzzles. Hope that is of use
One simple technique is a "checklist". At minimum for the "hung piece" problem, your checklist needs to contain: 1) Check all my pieces on the board for whether they are currently under attack; and for those that are, whether they are sufficiently protected. 2) For the move I am considering, am I moving my piece to an attacked square, and if so, will it be sufficiently protected there also? 3) For the move I am considering, am I removing protection from any other piece, either directly or by discovery?
Another very common way to drop pieces is via forks, so 4) inventory all of my pieces which have no protection (are loose) after my candidate move; does opponent have any move which can fork two of those?
You seem to be fixated on giving checkmate when you have the advantage, at the expense of other goals, including protecting your own pieces.
When you have an advantage, you should (usually) be chasing your opponent's pieces, not his king, and trying to force exchanges. Once you get into that mindset, you will do a better job of realizing whose pieces are attacked.
Your goal should be to get all your opponent's pieces off the the board so they won't be a(n unexpected) threat to you. Then your advantage, of a piece, pawn or "position" should win for you.