Actually, I'd remove the planks. Not sure what their purpose was. Anyway, if the subfloor is truly 1 1/14" ply, I'd put the backer over that. If you install the CBU over the planks, you'll have a situation that I personally have never encountered.
When you install CBU, you use a 1/4" notched trowel and spread thinset over the subfloor. The CBU is laid over the thinset and then screwed down. The seams are addressed as I mentioned.
So now you see the issue of the planks. If there aren't any gaps between them, I suppose you could put the CBU over them. However, if there are gaps, the thinset will fall through and you'd need a lot more thinset to make sure the CBU has a firm base to reside on.