40 year old slab-on-grade: insulation under new floor – GreenBuildingAdvisor

We are replacing the floor in one room of a 40-year old slab-on-grade house.  Right now, the slab is fully exposed. The distance from the slab surface to the finished ceiling is exactly 8′. There is no vapor barrier or insulation.  The heating climate zone is 5B, and the moisture regime is B. Two of the four walls in the room are exterior walls. We are not planning to do anything to the walls.

We are looking at engineered hardwood for the new floor. What is the best way to get some insulation under the new floor while minimizing the floor-to-ceiling height loss?  I’ve seen the insulation question asked before, but some of the solutions would probably leave us with a 7’6″ ceiling, and others are not for the slab-on-grade situation.

Given materials  and technologies available in 2025, what do you suggest?

Thank you.