Yes. I think the correct standing position, and how often you change it, will depend greatly on the conditions. The position shown in the video would be way too far forward if there were e.g. waist-high or peaky bumps. In fact, it would be impossible. The key is not to look, I think, at the position you are standing, but what the nose is doing. It wants to be skimming the water, not sticking right out of it nor, obviously, ploughing.
The correct position for this, and especially, how much you move, will differ hugely according to the conditions and board. In this first vid below, one of my favourites, these guys' feet seem almost rooted to the spot a lot of the time – necessarily so since they are using rudder steering. Long periods go past without any foot movement at all, and when it does come, it is only a few inches unless something very extreme is happening. They can catch the bumps in the rudder steering foot position, which is quite far back on the board.
They are of course pretty much all on SIC boards, in Hawaii. NONE of them move their feet very much. Mostly they can DW extremely effectively just by keeping one position, with their front foot on the rudder.
Contrast that with this video of Ivan in South Africa. Different board, different conditions, and a whole lot of foot movement.
And here is a less extreme example from Cape Town, but still lots of foot movement, and they are generally following the principle of getting as far forward as you can (i.e. without losing momentum, or ploughing) to catch the bumps, and then as far back as you can when riding then (for control and speed; again , how far back is determined by staying on the bump, too far back and obviously you will stall).
I have had the Coreban Dart out both in the tiny conditions shown in the video on this page and also in the larger of the kind of conditions shown in the Cape Town video. In the small conditions I was pretty much forward as shown in the OP vid, and wouldn't move more than a couple of inches back once on the bump – conservation of momentum being everything in those conditions. In the larger (very peaky, white-capping) conditions I was standing to catch the bumps about 30cm (1ft) behind the handle, and then once on the bump my back foot was on the kickpad, right at the rear.
This issue is one of the reasons why ruddered boards don't *always* seem to work so well in the short period DW conditions we get here. They commit you too much to one spot, and that spot is dictated, I suspect, by what works for Hawaii (especially Maliko), not what works for largely locally-wind-generated and heavily tidal chop in very shallow waters. The standard “Hawaiian” position is in particular often too far backwards for the smaller conditions we get here. The footwork of the people in my local area is MUCH more like Ivan's than Andrea's – and that is pretty much true of whatever board they are riding, so I don't think this observation just reduces to a 14ft vs. UL difference.
In fact, it's pretty much all about the footwork around the conditions I have here in the UK. I just don't recognise what Andrea, Mark, Connor etc are doing in the first video as anything like what we are doing in our local conditions. They are catching and riding bumps with need for hardly any foot movement. That just doesn't seem to happen at all for us.
But maybe I'm just doing it all wrong...I swear that there's just a couple of points where I find myself looking at e.g. Andrea and Mark in Bill's video and thinking “you'd have found that easier if you weren't quite so rooted to that steering pedal”. So clearly I am missing something because these guys are the best in the world. You do tend more to “pilot” a UL board rather than “surf” it as you do a 12-6 or a 14, for sure.
So different conditions, different boards, and differences in personal styles dictated by an interaction between the board, the conditions, and physical characteristics, will make a huge difference to where you stand and what you do with your feet, I reckon.