This is going to be a little story about electromagnetic interference (EMI). The good thing is: there will be a happy end :)
Having installed all the WS2811 LEDs, I decided to play a quick game to see if everything is still working. It was quite surprising to see the LEDs flicker like a Christmas tree, even though they should have been dark. This happened everytime the flipper coils actuated. Clearly there was some kind of EMI problem, inducing noise on the data line of the LEDs.
A quick scope measurement on the solenoids revealed the issue: