Okay........can anyone tell me why it's possible to glue down a 3/8" or 1/2" solid hardwood over concrete, with radiant heat, but not a 3/4" solid? Wouldn't the 3/4" be more stable?

No, more vessels to swell.

You walk a fine line even gluing thin solids to concrete.
They say it can be done, and it can, but the failure rate is extreme!!!

Concrete has moisture. Wood, especially solid, is a sponge to moisture. Causing cupping and buckling.

Engineered cross-ply are made especially for concrete, although they can and are put over plywood, also.

Personally, I think gluing down any solid to concrete is a bad idea. Our inspectors here (Perry and Ray), say this is one of the most common failure claims. That should be enough to convince one not to do it. The NWFA and NOFMA do not suggest gluing down solids. In fact, they specifically say solids MUST be nailed down (it's in the manual). Now I know some thin solids say you can glue them down (Bruce Natural Reflections and some others) but the point is, solids are never as stable as engineered and concrete will always emit some moisture. While the newer concrete sealing formulations may negate some of the vapor transmission, there is still some risk involved. IMO, engineered is the only flooring that should be glued directly to concrete with the single exception of 5/16" fingerblock parquet.