Using bow thruster to steer while underway

Mmm... I'd say barely rather than definitely - if she's catching them at all.
Just focus on the brief part of the video at 1:08, when the camera looks on stbd side.
But of course, waves alone are nowhere near enough to estimate the current.

In fact, since you are familiar with that area, I was wondering something that you probably can answer:
Looking at the map, the boat is heading W while going through the cut.
Now, do you have an idea of how fast a westbound current can move in that cut, at worst?

CJ, I lost count of how many times you ask how many boats someone else ran.
Let me try to address that once and for all: you ran more boat of any kind than myself, all other forumites, and just about any other boaters on the planet.
Happy with that?

Frankly speaking, your approach seems to me akin to someone pretending to be a sommelier after drinking three bottles of wine per day throughout his whole life.
But it doesn't work like that: understanding of quality is what really matters, quantity is only good for triggering cirrhosis!

Ok, in this case my previous theory (that also Capt Ralph envisaged) of unresponsive rudder due to a too low STW doesn't hold water, so to speak.
Oh, well. I wasn't thinking to place an order for a N63 anyhow!

I think the speed fluctuation indicates the vessel is going with the current yet slower than the wave period. The waves are building and shortening in period as he enters the "shallows", and his single screw is being overwhelmed by the quartering/following waves. As he cannot steer with throttles and has no chance of keeping the bow on the heading, he's trying to compensate with the bow thruster. He does seem to be oversteering and reacting instead of anticipating the swells. The boat certainly doesn't seem to enjoy the sea conditions.

Videos may have just saved me a lot of money. I think I’ll be scratching one of these off the list and stick to a big SF.

Indeed. Aside from agreeing with your summary, I believe another important factor is the one about stretched Nordhavns that JWY already pointed out, and I hope she doesn't mind if I extend it a bit.
In fact, interestingly, it's like in Dana Point they are the first to be well aware of the inherent flaws in the hull stretching exercise: try to find full (i.e., inclusive of the hull bottom) drawings of their stretched models, if you can. And this is from someone who used to proudly publish complete drawings of their boats, in the past... 'Nuff said.

I am attaching below the only example I ever came across of a comparison between the stretched version (N52, above) and the original hull (N47, below).
If someone has a similar drawing of the N63, I'd gladly have a look at it, but I'm pretty sure that the principle still stands.
Now, I don't think it takes a naval architect to understand that the one and only logic behind taking a 47 feet mould, make it longer, move just the rudder a bit further back, and sell the boat as a 52 footer is that the latter can fetch a higher price.
I mean, it's either one of two things: the 47 design was wrong, or the 52 extension is.

And by the same token, the N43 went through the same maquillage and became the N475, suggesting BTW with such name that it's somewhat bigger than the previous 47, which she isn't - also because the 47 in the meantime became a 52, as just explained. Ain't marketing a beautiful thing?
Back to the 63, as JWY said, she actually comes from a 55 hull, initially stretched to turn her into the 60, and then into the 63.
And the very same trick was used also with bigger models.

Of course, I can't tell how much that is relevant to the boat behavior in the OP video. Who could?
The only way to tell for sure would have been to have the original 55 doing the same route at the same time, and then compare the two videos.
But I think it's safe to tell, as also JWY inferred with her "bit of prejudice" (very kind of you, J!), that these marketing-driven stretched boats can hardly bring any improvement to the original design.
And to my simple mind, it's pretty obvious that anyone who should design a 52' hull from scratch would never place the propeller and the rudder where they are in the drawing below, if it weren't to avoid the investment in a completely new mould.
The same goes for the 475, 60/63, etc., obviously.

I would caution against making any assessment from that video alone. Too many unknowns to make any real determination.

Stretching the hull generally adds a lot of bouyancy in the stern, since the stern extension usually doesn't have a lot of weight over it (just a cockpit, or larger aft deck). This is generally counteracted by adding additional tankage (water/fuel) to help balance the boat, or in the case of the 60' defeaver I ran which had a tendancy to do a 180 degree turn in 2 boat lengths and try to throw you out of the helm seat if you were at hull speed and hit a counter current, they simply threw 2000 lbs of lead bars in the center bilge of the stern and put teak slats over it. What happens is the bow digs in and won't go faster yet the propellers are still trying to push the boat forward, so the stern wants to come around. Sort of like a fast rwd car in the rain and you give it a little too much throttle and the stern wants to swap ends with the front. This phenomenon tends to really amplify itself on displacement hulls as hull speed is hull speed, some planing hulls do exhibit this if you get the stern too light, but generally not as bad.

Not sure I have experienced what CJ is talking about, but the bottom line for me is that if a hull gets extended it's usually because it is determined after the fact that there needs to be a greater LWL. Improving the ride and/or handling with the extended LWL would be even better if the running gear was re-located appropriately.

You shouldn't be using the bow thruster at all when the boat is underway and doing more than 2 knots. It becomes greatly in-effective and is very hard on the bow thruster itself. As the bow comes up and down in waves like that, the bow thruster propeller(s) (suck air) get loaded and unloaded and it's a surefire way to bust the sheer pin or the thruster itself. Any vessel should be sufficiently ruddered to steer properly at 3 +/- knots or more underway.

The running gear is almost never moved when a hull is extended, at least 99% of the time. And, these days with CAD/CAM modeling, tank testing and everything at a NA's disposal, they should get the hull design right, right out of the gate.

I've been on at least 100 boats that were extended, either at the factory or after the build. Only one of them, out of all of them, runs/handles better than it's original design.....the 105' Johnson versus the 86' (which had a 23' beam and would run bow high, full plow wallow 13 knots at cruise). The 105' with 2000 hp 16v2000's got up on plane and ran 20-21 knots at 80% and greatly stablized the hull.