I unfortunately have broken most construction forms of directional kite boards and would like to say that both Carbon as well as Glass fiber boards tend to break when pushed to far.
A foam-core will break quite easily ; even when covered with carbon. It's the core that supports
the skins . The way it works , is the Core material, holds the outer skins , rigidly
in space. If the skins are allowed to move, relative to each other, the one under
compression, (the top skin) will usually buckle , before the one under tension, (the bottom skin)
In your case --Fly-away--
I think you need a directional that has at-least 3 surfboard stringers from nose to
tail made with 1/8 or 1/4" Douglas-fir marine ply or better, with 6-oz carbon on both sides
of the ply at (+ - 45 deg) AND some 50-K carbon uni on each side of each of the stringers.
Most of the grain on the ply , goes vertically between the skins. This lay-up can be done
before the new stringers are cut-out, and glue them in after cured. Use peel-ply on your lay-up.
That will transfer the compression from the outer skins and make your board a LOT
more difficult to break !
Do you know a surfboard-shaper ? Have it shaped after you add the stringers ; and vacuum-bag
your own carbon skins on it.
Carbon is NOT worth the extra money, unless it's used Properly !!!
Carbon is actually more Brittle than fiberglass, (for the same weight) ; that's because
you need more layers of glass to get the same compression and tensile strength
as carbon, (so the carbon ends up being thinner).