I'm not an engineer
and I've never played one on TV. But I'd have to think laminating in a sheet of cf or anything else is going to be a great waste of time and material. If you want to stop flex, you cdon't add another sheet, since sheets
by definition will be flexible.
You would laminate a couple of tubes or box beams onto the area that is flexing too much. Beams or tubes will be tremendously stronger at resisting the flex, when placed with their axis (length) running in the same direction that you're trying to stop the flexing in.
If you want to use a sheet of cf? Take some PCV pipe or paper towel tubes, laminate them with the cf sheet so you now have a stiff cf tube, and before it cicks off, laminate that into the surface you are trying to stiffen. (Gelcoat ground off, because it may let go before anything else does.)
Beams, not sheets
. Stick of two by four if you don't want to use the cf at all. Ten bucks worth of aluminum
square tube if you want something light and easy.