Tile – What are these ‘cabochon’ tiles called in English

Here are some good points against using plywood, the source is talking about tiling a floor but most of the points are valid for walls as well.

In my opinion it's better to go the "overkill" route, then have to redo the job in the future because something didn't turn out right.

The cost difference between plywood and cement board is negligible, so your not going to save any money using plywood (unless you already have it).

Do the job right and use cement board, when you don't have any problems and you can enjoy the tile for years to come you will never regret the decision.

I would probably use unmodified thin set to cover the gaps and give a good base for applying the tile.

Could you do something a little decorative and use a border tile around the repaired area, sort of like a picture frame? Then use a different tile to fill in the area. The border would make the change in depth harder to see.