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“The final question is, is there any reason that a ground rod in the basement floor would not be recommended for radio purposes?”
None at all. Ground is ground, outside or in a basement. In fact it is better in the basement as you have a head start in depth from the basement itself. The deeper the ground rod is, the better moist dirt you slam the thing into, in turn better conductivity for the return path.
Same is true if you hammer in a 20 foot ground rod. It goes deeper into the dirt for not just more surface area to make contact with the dirt, but into the better dirt deeper below the surface. It has more moisture and if we examine elementary electrical physics, water conducts…as does something moist…including dirt.
This is why there is recommendation to all Part 15 3 meter stick operators to keep that ground system in check and often recommended to water it like watering the yard.
They say that water is not good for anything electronic or electrical. But in the case of getting the maximum ground conductivity out of a ground rod and radial system, water and moisture in the dirt is your savior.