A GFCI detects an imbalance in current, not volts. You need 3 conductor + ground for this setup to work as designed in scenario #3. I like scenario #2 if you don't have 3 conductor cable installed.

Bigbird - Why 3 conductor?

This wiring is not yet run. Literally 5 foot from panel to through carflex to outlet box for pump (not yet installed)

2 hot wires from GFI breaker to terminals 1 + 3 of the Timer located in the panel.

From pump: 1 Hot going to terminal #4 off timer in panel. 1 Neutral goes to 2pole GFI breaker and of course the ground to ground bar. Where does the 3rd conductor come in?

With 220v run you have no neutral. The 2 wires are both hot wires and only supply 220v you need the third wire as a neutral to supply the 110v you need. you go from one of the hots to the neutral to get the 110v.

One other option would be to have a 110 supply there and a humungous 220/240 ac relay to switch the pump on so the 220 v supply just triggers the relay, not sure how satisfactory it would be owing to the huge current draw when a motor starts, but a thought anyway.

Since the clock motors are probably a very small load, a 120/240V transformer used as a step up should easily supply the clock motors.
Expect a relatively short life from the pump motor at 120 V.
The starting surge will be large and prolonged since as the impeller tries to come up to speed the load on the motor increases.
240 V motors are not more efficient (power is power at 120 V or 240 V).
The current decrease on the 120 V motor allows for even #14 wire to be larger than is required, reducing the voltage drop during startup.