Why birch ply? I would have thought (potentially naively) that most of the appeal is in the end grain, which won't be seen in your application. So you may be able to use a cheaper veneered alternative to get the same look?
If it has to be ply, why not 6mm. It's not ss if it's structural.
Or particularly hardwearing as a floor material...
The heating mat manufactuer would be able to tell you if ply is a good choice ornot too.
@NotThamesWater started
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Why birch ply? I would have thought (potentially naively) that most of the appeal is in the end grain, which won't be seen in your application. So you may be able to use a cheaper veneered alternative to get the same look?