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Beading will also cover some other sins on the interface on the other edge that is not cracking (I assume that because it is a smaller piece of MDF on that side, a few cm instead of a couple of feet, so the movement is less due to less material to expand across its surface) but is a bit of an ugly edge.
Prime with cover stain and paint with the eggshell of the cupboard then pin to the cupboard face without fixing to the wall?
Cheers. Initial rounds of discussion are leaning towards the beading, which might be the easiest option also. But good to know this info if she, I mean we decide the beading is not to our aesthetic tastes.