You could do it with a lone 2 pos. e unit + 2 isolated rails. You can use what you like really.
You know some agricultural equip? Relays, saftey loops, etc.. Your general "switching & wiring knowledge" is still pretty applicable. Mostly; wiring is wiring, (and switches included....: isolated rails are just a funny switch ))
Staggered movents, but they just sort of "catch up" to the original starting position and continue the cycle from there
It requires a powered block beyound the stopping block that is long enough for the trolley to reach bump speed from a dead stop; and the isolated rail needs to be centered along each stop block.
A delay is only needed at stops where there is one trolley/siding !
Where there are two trolleys/2siding at a station, one has been sitting waiting, loading.
Here's your story, keeping in mind the flow of people is greatest on exit and a good station flows well.... Insufficient funds forbids upgrading the amperage capability to your traction line and it is only designed to run one trolley at a time, but for station efficiency they use two! For a P.R. spin it is also billed as a conveince and saftey protocal only one trolley moves so a wreck can never happen and you can wait for your departure sitting in the windfree shelter of the trolley cabin.
T-1 arrirves back and t2 leaves immediately. T1 waits for its next departure. t2 come back; unloads. While the platform is full of #2 arrivals, t1 bumps and stops; now staged for departure but waiting breifly for stragglers while t2 bumps and stops now ready to load, so t1 leaves........
With two, 2-siding stations and two 2-position e units, you can run three and they will "juggle" platform postions.
You might even be able to work this out via the anti derail features on the turnouts.... I'm not awake enough yet..... maybe later...