You can use the same technic presented for animating W noise seemlessly, to get the spatial noise map to be seemless along the Y axis. In https://www.youtube.com/watch?v=1C8jPPRHej4 I used this technic for the roughness and also to mask the bump. basically mix the same noise texture offset along Y axis by plan size and use the Y coordinate as the mix factor (scaled to fit between 0 and 1). (also had to use a modulo operation to get the coordinate to repeat for each plan since I was using object coordinate, but you could probably avoid it by using UV).
Also found an alternative solution on reddit, which is to map the Y coordinate to a circul in the Y/W space by doing y=cos(y*s) and w=sin(y*s) scaled so that this y*s is a multiple of 2*pi for the plan size.
