Regarding scoop, yes they can provide some comfort or reasureance in the stance.
I have had varying amounts of scoop in boards recently, and found that it didn't make much difference because of the way I would stand quite often.
Certainly on flat water I would stand a stride the board & the feet would be on the edges of the scoop giving a good feel. But in rougher water I would find myself going to my natural surf stance to a degree, for max balance, this is not optimal for racing obviously but it's the most comfortable for me.
Standing with a surf stance, I'm on the bottom of the scoop so its flat, or like a flat deck, my C of G is lowered by the depth of scoop, anywere between 6mm to 60mm, bugger all in comparison to bending the knees & dropping the torso when digging deep in a powerfull stroke with a short paddle, a far greater lowering of C of G.
I haven't found any signifigant gain in stability worth the effort of carving the scoop, particularly with this latest board, it's a hybrid, surfboard & canoe or plaining hull aft that gains stability from it's width & flatness & canoe that shears through water instead of lifting or trying to push over it.
When on a runner the stern of the board will reduce its wetted surface area as it gets on the plane, where a canoe stern won't, I think thats where the speed difference will be realised.
In flat water paddling it has been long proven that k1 & C1 hulls are the most efficent...but we would have a little bit of trouble standing on them

ps...Sorry got a bit off the subject of scoop here, I may use a deck pad with slightly turned up edge in the optimal paddling area, like Naish had on some boards.