I have posted this before, I apologize if I sound like a broken record. You need clamping force or friction. A little of both or a lot of one or the other.
Assuming your hydraulics are functioning properly, it sounds like you don't have enough of either.
Do carbon brakes actually generate more braking power? Serious question. I looked around a bit and didn't see anyone that states that these brakes have a higher friction coefficient. They are lighter, and last longer (

), and can handle more heat than iron rotors, but do they actually stop better?
Get a pressure gauge and hook it to the front brakes and see if how much line pressure you are building. Check it a 3-4 times with moderate pedal pressure and then 3-4 more with all you got. With line pressures a known we can come up with a clamping force at the caliper.