There's a right way to court the center and a wrong way to court the center.
The wrong way is to take whatever position you think they hold at the moment. This doesn't work because it's hard to figure out exactly what positions you need to adopt, and the center, being fickle, will change on you. Overall, you'll wind up looking weak.
The right way is to take positions that you believe in, and then convince the center that you're right about them. If you can do that, then you're on much stronger ground because you can get the independent vote and appeal to your base at the same time. You'll also force your opponent to try to play in enemy territory, so to speak.
I agree with your "right way to court the center." It needs to be the Right's way to court the Center.