Electrons don't move faster or slower (for all intents and purposes, of course things can vary in nature a bit though...).
THe analog I use is the pressure of water in the pipe is the voltage, and the flow rate of the water in the pipe is the current. if the water pressure isn't high enough to push through the narrow pipe, then not all of the water gets through. Simple as that.
Nothing about the water getting slowed down because it can't push hard enough or whatever (sometimes used in the car-in-a-tunnel analogies). Those just confuse people because it implies electrons move more slowly in the resistor than in the wire. This would cause a build-up of electrons inside the resistor until it exploded, in the same way a funnel overflows if you pour water into it too quickly.
It's similar to your strong men analog, except the current is the number of men going through the doorway at once, rather than the weaker ones getting slowed down. If you can't push hard enough you don't get through at all.
I like using the flow-rate of water or the number of men going through the door at once because it explains how current can be split down two wires and why voltage is the same across parallel connections (there is a loophole to this analogy though with parallel resistors of different values.)