Plummet said..
What makes a good TT for the waves.
Rounded tips, Reasonable rockerrocker. Conmcave, tip flex and stiffer center section definitely is better.
Plummet is so on the money. I got myself a
Jimmy Lewis Model III very recently. 2 x sesshs in so far and I am loving it!

Have been riding very similar boards for years - Liquid Force Drop 136/Proof 140/Proof 151 - all extensions of Jimmy Lewis' dominatrix concave with round rails, narrowing to sharp at the, slightly narrower than most, tips.
Whilst these boards are not quite as cushy as say a North x-ride/Shinn Monk etc, you just can't beat the shape for TT in the surf. Monk and X-ride are a goodies too, but still essentially square rail TTs.
If you dig surf style TT then you owe it to yourself to suspend 'old designs/construction can't be any good' mindset and try a JL or LF round rail board.BTW - the Model III has been a step up all round over the heavier LF proof boards. So sweet.

Acceleration out of heavy turns is just too much fun!
Advise you
step up half a size from your normal TT as the tips are not as wide as conventional TTs. (Don't sweat a couple of cms longer, I've been riding a 151 for years and it fangs)
I'm 84kgs and the 140cm Model III goes shweet for me and bottom end is fine (but best with slightly overpowered 10m Lithium in 18-21kts).
Disclaimer:
Paid full price, no affiliation but I had some trouble getting hold of a model III in Oz until Jas and Sonya at WOK came through for me.