So, my Godox AD600 and all my Bowens S-mount adapters technically fit on my Matthews C-stand's stud, but it was a wobbly fit. Thanks to someone here, I learned that what I needed was (rather un-intuitively) a "Kupo Baby 5/8" Receiver to Stud Adapter for Elinchrom Heads" to make the connection a solid one.
So I got one and it worked perfectly and now I'm happy, and I wanted to say thanks to whoever it was that posted the info - I don't know who it was, as my attempt to locate the original post failed. Never in a million years would I have figured out that was the name of the thingy I needed.
Also, in general, I really appreciate all the graciously-offered expertise and advice you folks provide on this forum. I now return to my default lurk-and-learn mode.