Thanks for publishing this work, xsvtoys . I've been using this thread extensively over at least the last six months as I work on-and-off to get my Monte Carlo working. The deep dive step-by-step into the startup process was essential to finally getting to reliably start a game every time I push the credit button. The logic you present is sound and applicable beyond your target game (Bon Voyage). A little tip for those who find this thread - some things in startup happen fast; I used the slow-mo video on my phone to watch the ball count stepper which is where the core of my game's issues resided. Slowing things down can really help sort it all out!
For what it's worth, I think the resistor is there to minimize EMF. When designing that circuit, first choose a coil that will drive the lockout mechanism, then pick a resistor that will block just enough voltage so the coil can't pull the mechanism. Lacking the resistor, the step function change in current will cause the EMF to pulsate like the damped motion of a diving board. Maybe the designers found the 'ringing' in the coil could bounce the lockout lever? In that case going from full current to less current reduces the size of the step function and therefore reduces the undesired EMF which would prevent the postulated 'bounce'.
-Rob
-visit http://www.kahr.us to get my daughterboard that helps fix WPC pinball resets or my replacement LED score displays for model H and model S Skee Ball