Crack repair - gypcrete floor

I'm looking for informed comment and/or advice on a plan to repair cracks in my 1-1/2" thick gypsum-based (gypcrete) floor.

Problem: The floor is broken up into fairly large sections that are separated by hairline cracks. When I walk on a section, it moves just a tiny bit, causing its edges to rub against adjacent sections. This results in annoying crunching and crackling sounds.

Objective: I want to eliminate the crunching/crackling sounds without the big expense and hassle of pouring a new gypcrete floor.

Assumption: A series of cement "plugs" along the crackline would provide the rigidity needed to prevent the sections from moving and rubbing against each other when stepped on.

Plan:

Drill 5/8" holes every foot or so into the cracks along the crackline (ie. not across them). The holes would be drilled at an angle of 30 degrees. The angle would alternate -- drill one hole at

30 degrees in one direction and drill the next hole at 30 degrees in the opposite direction.

After the holes are drilled, push a layer of thin plastic film into the holes to line them. The liner would keep the existing gypcrete separate from the new cement. The gypcrete and cement must be kept separate because the moisture from the new cement will break down the gypcrete and these materials are chemically incompatible with each other.
Squeeze quick-setting cement tightly into the holes and stay off floor until cement hardens.

Considerations: Since the gypcrete is meant to prevent a fire from burning through the floor into the wood structure below, the "plug" material must be fireproof and have roughly the same heat-transference properties as gypcrete. Cement is used instead of gypcrete as a repair material because it's considerably more resistant to shear stresses than gypcrete.

Thanks in advance for all helpful replies.

Darro