Thanks to all who helped troubleshoot.
In the end, it was determined that the brand new solenoid installed in August in La Rochelle had become unreliable ("glitchy"). Towards the end, it was failing about 9 out of every 10 times.
And so a new solenoid was installed on Saturday. The engine has been started flawlessly about 20 times since.
The reference for the new 150A solenoid, which is the same physical size as the Amel factory original, but with the downside that it does not have the pushbutton functionality at the top:
Made in Brazil
I also obtained a spare, 100A, same physical size as the Amel factory original, with pushbutton functionality at the top (same as Amel factory):
Made in Taiwan
By the way, the solenoid installed in La Rochelle in August that failed was a 5-second solenoid, 100A:
HC Car Go
133695 - Solenoid
Holger Christiansen - A Bosch Group Company
Made in China
Finally, some of you may recall that our "STOP" button was, confusingly, not stopping the engine about 30% of the attempts. We replaced the original Yanmar with a standard industrial waterproof "Stop" button (red, same size, flexible transparent waterproof cover above the button). So far, we've stopped the engine each time every time, about 10 times.
Cheers to all,