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Anyone knowledgeable on stoves, fireplaces, hearths?
Yep. Burny! Don't touch.
I measured, and installed my slate hearth whilst my fireplace looked much like yours does - although minus the pile of rubble where the hearth would fit. It was half a dozen large slate tiles sitting atop a concrete base. I then plastered down to the hearth and fitted skirting outside of the fireplace aperture.
Inside the fireplace aperture I covered the vertical surfaces with fire cement all the way down to the tiles and the Stove kinda obscured the area well enough for it to look very nice. This area was especially well obscured after I'd piled up fire wood in the area's to either side of the Stove.
Like this but wood was both sides of the Stove and my plaster ran up to the aperture...

