A 13T front gear is not going to give you more power. It will move the power you have. A smaller sprocket will lower your top speed a little, but should help with that area between 2nd and 3rd. With the mods you have I would only gear down if you rode really tight trails or raced a really tight MX course. You should be making MORE then enough power to pull stock gearing up any hill. Shorter gearing will help with the holeshot in drag races, but will lower your top speed, slightly. I guess it would depend on the steepness of the hill and the length of the course. There is only one way to find out. Buy one and take it with you and test, test, test.
There is an idea that makes sense and is quite common in the snowmobile world. My snowmobile is geared for a top speed around 100MPH. Will it go that fast, not really. Do I want to go that fast, not really. If I gear down for a top speed of 80MPH my motor and clutch will not have to work so hard. It will pull like a tractor and take off like a dragster, but the top end will be slightly slower. It is a small trade off, and most people find it worth while. Lets face it, unless you are on a long smooth lake, 100MPH is too fast. I would rather climb to the top of a mountain in waist deep snow anyway.
On top of the swingarm at the back, there are little notches. You use them when you tighten the chain. I think they are there to keep the swingarm and axle aligned. I should be getting the 13T sprocket soon and I will keep you posted. Has anyone had to tighten their chain? Mine seems pretty good still, little to no stretch and it has been ridden hard!