I assume you ride upwind with your rear foot in front of the strap ?
If not, that is a huge problem and the reason why you dont feel it works in light wind....
Getting a bigger board wont help regarding DTL, but it will be worse.
1. Front footstrap, HAS to be set one plughole further apart, so you can angle the foot and has full freedom.
Often you will slide it toward the windward side when going upwind.
You should NOT put the front strap too far forward - as you can ride with more speed and dedication strapped, and also change weight distribution much more and better - so you can control everything with a slightly more rear position than if strapless.
2. Rear footstrap is personal liking only.
It should sit quite tight for my taste though. Some like wide straps with more foot movement possible - but not me, I find it is a very wrong and sketchy feel, especially for really powered aerial of the lips.
But the position has two ways:
a. Beginners mount it quite forward, so they can always ride in the strap DTL (OR, for light wind but quite big waves).
b. Experienced mount it at the "perfect" spot for DTL riding when steep waves and good speed.
Then, in light wind or big kites or flat waves, you just ride DTL standing in front of the rear strap - really good and extremely fine hold this way, so the risk of sliding/crashing is close to zero - and you get huge glide.
So two things IMO: Dont go with a bigger board ! The front strap quite forward, but NOT as much as if you rode it strapless - it will feel bad
Then there are other individual preferences.
I like my straps to sit "well" not tight but quite firm still having the option to move/twist.
Others like really really big loose straps - you could try both to see what suits you.
But the whole idea of strapped riding, is to find a board where you can control everything around the "power" point, namely the front footstrap - and then the rear foot position can change according to conditions or liking.
In really light conditions, you just step your rear foot further forward than just in front of the rear strap, and you have by far the most efficient way of going upwind (narrow stance and strapped so more control/speed).
I think the 5'6 whip you got is an okay size, if you are medium weight Mark.
In small and not steep waves, and less wind, straps does not matter and you might be better off strapless, in order to enjoy an otherwise boring session maybe....