sandstone needs to breathe whatever.
a 6 or 9mm ply stuck up with adhesive would do and finish with a small quadrant or something around the edges.
9.5 mm plasterboard would be better if it’s bone dry plus you can plaster it all in.
stick it up with generous blobs of multistik adhesive and prop it up overnight.
you’ll still need to stabilise it first and/or blob it strategically where it’s most sound and/or least ropey.
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