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Flexibility is useful for coping with different thermal coefficients of expansion.
If the filler is lying on a solid floor, in effect a giant heat sink, it will experience less temperature variation than the marble slab exposed to the temperature in your (living?) room.
Now there is a woodburner, (raised legs?, clearance from floor?), confirmed the hearth is likely to experience an even greater range of temperatures.If you do choose 'mortar' do you have any PVA to use in it to help prevent shrinkage cracking?
I think there's an element of (albeit vertical) slump to plasterboard adhesive as the recommended dollup thickness is huge, 50mm from memory. Also not sure why it would require flexibility when cured.
I think I'll just use mortar. Cheers.