There are two very different ways of going upwind on surfboards - and both works !
1. You can ride the board flat and more on its fins
2. Or you can ride the board on its much longer edge
In both cases, feet close together is good, as Starsky also said.
You never ride a surfboard like a TT, even when "edged".
But either more like a raceboard (#1), or like a surfboard (#2).
Both ways works extremely well, and go good upwind.
But REALLY really different in all aspects !
It depends on the board, on the water conditions, on the kite, on the board setup - and the rider - what works best
Keeping the board flat and riding on the fins, works most often well in really light wind - to get planing and KEEP IT GOING in lulls
And here you can gain a bit upwind by having bigger fins - just like raceboards do.
But for upwind, I think that riding with your weight much more forward, and keeping most of the windward rail in the water - works extremely well for going upwind
Now you can glide without too much speed (speed is not good for upwind), and with a very low planing limit - so you dont need as much kitepull (more depower is good for upwind), and you can even cross chop very comfortably - because of quite low speed and the most efficient glide.
And also because the board is not flat (where it would be "hammering" into every little piece of chop if kept flat), so it will often glide and cut through small waves and chop much better, when using the rail.
Another plus is that fin size does not matter - you choose the fins that will give you the best personal wave feedback when doing bottom turns and cutbacks - and nothing else but that. Which is usually quite small - for best "ride".
But depends on the given conditions, and is different for different days and spots and wind - so how much you angle your board is related to the water surface too.
I think you can actually get planing in less wind with the "race" method (#1) - but you will most likely go faster upwind with the "surf" method (#2).
Up to you to find out - would just mention these two VERY different techniques most are using
PS: Does not matter if strapped or strapless - above goes for both, although quite difficult with #1 if heavy chop and strapless.