You seem to think you need an asbestos-free cement board which is what all these links and suggestions point to. Fact is, they are the default solution for roofing and wetroom use. The primary difference between them and asbestos is that they use glass fibre instead of asbestos, although the tile backing boards are less like asbestos sheets, having embedded glass fibre mesh rather than bulk mixed fibres like traditional asbestos cement sheets.
A shed won't have spent most of its time under the water line(?), so as a precedent it doesn't sound very convincing.
If it's largely underground, and cement board doesn't work, surely you should be looking at resin or plastic instead. Cement is cement, regardless of what it is mixed with and you seem to have convinced yourself it's no good.
Murray