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Concrete gravel boards cut down with an angle grinder would be your best bet if you go down that route as they won't rot out, your timber boxes will and batten will rot even quicker. Lay them on a membrane trimmed to size to avoid scratching the porcelain. That way you might even be able to move the beds around to minimise staining and fading.
Edit: wide damp proof course would be ideal for the membrane.
Thanks - assumed as much (and believe it's on flexible adhesive but will check). Will have a think about whether I could raise the bed a bit on battons or similar to help with drainage