By playing all balls through the putt you are developing short-putt confidence and strengthening your nerve.
You can use this to your advantage by conceding shots to you partners and opponents early in the game, then requiring that all putts be carried through towards the end.
This creates a false sense of confidence in them in the beginning, and they suddenly have to start hitting putts at a time when they are so crucial.
(Yes, this is taking advantage of people, and you may not want to do it, but it will give you a slight edge) this method was used by Walter Hagen to his advantage in the 1920s.
Many short putts are missed through simple carelessness; never take a short putt for granted.
It may be hard to view the putt seriously because it seems so simple, but don't let it fool you. Take every shot seriously, get comfortable and follow your routine on every time regardless of how simple it may look.
Anything inside of 5 feet is considered a shot putt, it is best to hit the ball firmly.
A little harder stroke than you think is necessary is good advice, and play for the back of the cup.
Doing this allows you to eliminate some or all of the break, and as you know, it is always easier to complete a straight putt, than a curved one.
If the side slope is severe, you may however want to play it more gently, as if it were a downhill putt.
As mentioned earlier, sticking to your usual routine of finishing all putts, will build your confidence and give you more strength and nerve in your short putts during games.