This is what I would do:
Keep the timer box in a dry area.
Use one of the side entries and use PVC piping (electrical) to pipe the wires to the outdoor rated receptacles that you mount in the stand.
Use THHN wires (6 black(hot leg) 1 white(neutral) and a green wire (Ground). I would tie all the neutrals together at the receptacles and the hot wire gets jumper-ed at the relays in the controller.
Since you are talking 6 receptacles, you may want to consider adding a dedicated circuit from the circuit breaker box.
Your wire size will depend on the breaker size used. If you use a 15A breaker, a 14AWG will be good. if you go for the 20A breaker, you must use 12AWG.
HTH
Waffleman