The canon evidence isn't clear though. All we have are second hand stories that it moves. There is no indication of what it looks like, how it moves, or why it moves.
I have yet to hear a plausible theory for how anything worthy of being called a "castle" could move around in the environment of the Neck.
There is clear evidence from the canon that even fairly modest sized longships cannot effectively move through the Neck. A floating vessel of any substantial size would be nearly impossible to move in that environment, and even if it were possible there is no benefit to doing so.
What you have said also doesn't address the magical angle. The only semi-plausible theory for something akin to movement is magical concealment. Concealing the castle magically would give the appearance of movement to those trying to find it. There is just as much "evidence from GRRM himself (via the books)" that points towards the crannogmen practicing magic as there is of the castle moving. In fact the magic is actually explained in much more detail than the claim that the castle moves. We get specifics about where the magic came from and the kinds of things they can accomplish with magic, including the very peculiar mention of using magic to make "castles appear and disappear."
If we are weighing evidence, on one side there is merely the vague and extraordinary claim that the castle moves, with nothing to back it up. On the other side are mountains of reasons why it would be impractical and probably impossible for it to move, and no counter-argument (other than magical concealment) to explain how it might be possible.
I still disagree. In terms of the legends of GWW its always been "the moving castle". It would be a significant disappointment to have it not move. Take the opportunity to make this project something unique and special, with an exuse to do so. I still like the idea of the boats from the previous project lead. Despite what any other disconnected canon there is of the project, what fans know it for is that it's the home of House Reed and that supposedly migrates. Take half of its legend and you're doing the project a disservice.
It is best to phrase it like this.
Suppose Atlantis is in the world of Game of Thrones. It's spoken and taled to be a sunken city-island said to house merpeople. The city is supposedly ruined but still functions properly, it's far east, off from the shores of Dorne. However, there are a few comments claiming they have the power to hide their island entirely, to make it disappear.
You'd be coming in and saying "it's not sunken" and "it's not ruined." Yet that is half the fun, the point, and the story. You pull that legend away from it and you've ruined the fantasy.
Look into the Uros of Lake Titicaca, the Phumdis of Loktak Lake. I also believe the terra should shift to look more like the marshes in florida. This would make it feasible that ships would struggle to pass, but plausible that the various islands could move about slowly. The Phumdis inspiration would also be accurate as they could be make made islands used for the purpose of fishing.
Either way, the "magic" seems like a shortcut rather than finding a reasonable excuse to have the legends be true.
All said;
I would also revise the palette of the castle entirely. It is falling under the salt and pepper appearance with the black basalt.