Good analysis.
To be clear though, the OP issue will occur with any type of widget , because the Stop parameter of the SAFP itself seems to engage when the value of any of those widgets reaches greater than 0.5. You can test it by replacing the button widget assigned to the Stop parameter with any other type of widget— a dial, a label etc. The same result will occur.
Thank you for this additional information. It’s helpful.
I used Playhead position because it was the only way I found to stop/rewind the AFP
The SAFP has all the controls but it is not multitrack.
I just don’t understand why the new MTAP does not have a Stop button neither, as it has all most of SAFP features 
If there was a Stop button in AFP (and in MTAP), it would avoid to use Agree that if there was some
What should a “Stop” button do that the Pause button doesn’t do?
The common behavior of a “STOP” button on a player is usually: Stop playing and return to start position (in one go).
BTW: Something that i also expected to be there since… well ever.
So how would one use this in practice?
How often does one need to just stop/rewind vs
a) Pause and continue
b) Stop because going to the next track
For myself, I’ve occasionally wanted to pause and continue, or I have wanted to just quick start playing again from the beginning (or from the last place I was playing using the Al Segno button) but I’ve never found it to be much of an inconvenience to press pause and then rewind.
I’m not sure about changing the UI at this point but we could certainly add a Stop parameter that would basically stop and rewind and that could be controlled by a widget (which is generally the way to manage it in practice anyway)
For myself, i am used to having this button (or at least that “functionality”) in almost every player (be it hardware or software) and i never understood why we didn’t have such in the GP-Players.
Of course i could press pause & rewind after each other, but this takes 2 clicks (two! 
)! It’s not a big inconvenience, but it just doesn’t “feel” right…
That’d be absolutely sufficient and something i would appreciate very much!
Is it worth pointing out that you can probably do this already in GP6 by adding two actions to a button - one to pause and the second to rewind?