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Shouldn’t warp or cup, especially over a kitchen cupboard door size. BB grade ply
shouldn’t have any voids or things that need filling, but the end grain will show through paint unless you totally cover it with filler. The grain will show through on the face if you hand paint them. I like that, may not be what you’re after though.Cheaper option would be MR MDF, hand painted. No chance of warp and no grain. Water based hand painted finishes aren’t the most durable though.
Kitchen cupboard doors: I can't find ones I like at a good price. If I get 18mm ply cut to size and fill/sand the end grain then paint and varnish the whole thing, will I prevent it warping?