I guess the reason why you are not happy with the results is because the camera is a consumer camera, which has it's limitation, due to that fact. After reading up on the camera specs, it looks like you will get the best quality when you set it to FXP (17 Mbps). And I'm guessing the color space is either 4:1:1 or 4:2:0, which is high compression to your color. And then you have to deal with the lens that is built in.
So you have a lot of things going against you with this camera. It will never match the quality of high end cameras. So with FCP, you will not see a difference in trying to render it out to a better codec. Stay native to whatever codec the camera records on. Try to see it like this, you may only five cars in a highway so it doesn't matter how many lanes you add if the traffic is low, they won't move any faster.