I did not know that the Coaster motors were originally skyrockets. Certainly, that's the classic mix and probably a correct assumption. However, it is possible to use the same tooling for all motors and three different compositions. Directions for speeding/slowing a mix appeared well over a century ago, though I don't recall which book. Throat measurements of the three motors would be conclusive...but as I said, you're probably right.
My mentor told me of one semi-authority who recommended changing the composition...of an APCP motor when it CATOed. THAT would be foolish, as it's far easier to simply redesign the motor slightly.
Related to your last paragraph: somewhere I have a letter from Frank Kosdon to my mentor, telling him to cease and desist selling snap-ring research hardware, as it was Frank's invention, etc., etc. The letter ended with a request for my mentor to please forward the letter to another person known to vend such hardware, as Frank didn't want to have to retype the letter...


But that was Frank.