I had done some research about those two projects in the past and the conclusion I was able to come up with is that those rerecordings that have been released dozens of times were done in 1981 in Nashville and subsequently licensed over and over again. I've found that these recordings were released in 1981 in Italy and the Netherlands, licensed from "Key-Seven, Nashville".

The "Dancin' In The Streets" album, also known as Rainbow, was released the following year [[1982). The copyrights on my copy mention "Southampton" and "Indigo Music" in Nashville as well, but I believe these were different sessions from those rerecordings.

The whole thing is still a bit of a mystery, but I believe motony is correct that Martha was likely paid a flat fee per track for all of these like Mary Wells.