Akinbo,
You stated that "Since you know G, M and r for Earth, I want maximum accuracy, give it to me please!"
Unfortunately, I do not know the number of free electrons encountered by any signal along its path. Since the travel-time of the signal depends upon this number, neither I nor anyone else can be absolutely accurate. I know, from personal experience, that that number can change dramatically in time-scales less than 0.001 seconds, for signals traveling through the Earth's ionosphere. This is a major source of error, in attempting to geo-locate signals via their measured travel-times, especially at low frequencies.
You stated that "Special relativity is being used to define the constancy and the value of that constant"
Special relativity only defined the former, not the latter.
You stated "I take you to mean that the law of the constancy of light in vacuo is invalid under (very strong) gravitational influence? And valid only where there is no gravitational field?"
"Invalid" is too strong a word. As you increase the content of (formerly) "empty space", by adding gravitational fields, free electrons, or anything else that light may interact with, then the speed of light traversing that space will increasingly deviate from its speed in "vacuum".
Rob McEachern