Chiming in a little late here, but the space behind the chimney would lend itself to styro-crete. Ground up styrofoam entrained in concrete.
I did that behind my fireplace and it seems to be working very well.
We are putting in a rock & cement wall above the hearth which we want to heat up from the exhaust gases, behind that is a styrocrete wall about 8" thick so that we minimize heat transfer to the exterior wall.
Styro or EPS crete stays where it is put, does not compress or shrink is termite and fire proof and easy to do.
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