Kazi, you got almost everything "against" you on this one
1. You want to use the same board for surfing and kitesurfing.
Eventhough some surfboards are also meant to handle chop like one says, there is still a huge difference.
Most can not use the same boards for surf and kite, works only for a marginal fraction of kitesurfers, and mostly some who are extremely good at surfing (small boards) or have "clean" wave conditions for kitesurfing where a bigger/wider chop sensitive board would work.
2. You "have just started kiting directionals" ?
Okay, from most other riders, experience says that changing from a TT to a directional does not work well in the start.
You ride the directional like your TT - which is totally and completely wrong in every way.
Most will ride with the board edged, and a lot of weight on their rear foot
To ride a directional, your front foot is the "power point" that everything is concentrated about.
If you have any TT feel left when riding a directional, you WILL experience a bouncing and feel really bad in chop - board
3. Last, but not least - the concave bottom ?
This is used by most kitesurf brands today actually (including my Ralf BachSchuster Custom boards).
But NOT used that much in surfboards, because the speed and need of control if often two very different levels.
If you use too much concave, the board will track fine and not "bounce" yes.
But it will also be stiff and not work/feel well in waves.
Then you can add rocker - but rocker might make a board more lively, but it actually (opposite of what many writes/thinks here) makes the board even more chop sensitive
Your current board is apparently one of the most difficult ones to ride in chop it seems.
Does not make it a bad board at all, and maybe you will love this board when you got #2 mastered ?
It could also be the opposite - that YOU need a chop specific board.
As one mentioned, the North Kontakt is one example of an awesome board for chop (but it is a more strapped riding board though), more narrow and narrow tail and not too much rocker and it has a concave bottom.
Many boards out there - but IMO not possible to find one that fits both for surfing and kitesurfing in one board for you.
Unless you agree with #2, that you are far from there yet ?
If correct, enjoy the "ride" and journey, because mastering a directional seems easy at first, but you will still have some REALLY bad habits from the TwinTip for a long time (like having some weight on your rear foot in bottom turns etc)
I am just "yakking" maybe, I know, but feel strongly about this and have lots of experience
Just want to help if I can