Having come to a halt, I think I must be on the entirely wrong track. So I thought about engravers, which I have no experience with. The NR Snippets section has this topic "Centering markup on note heads automatically”. If you compile this under 2.19.37 the markup is certainly not aligned in the centre. Why is that? It appears to be correct at 2.18.2.
More importantly, is using an engraver the approach that is required, and attempting to do it using grob parents and properties is incorrect and indeed impossible?
Andrew