First thought I have is that there is underground wire (conduit not required) available for which ever option you choose. The wire can be quickly placed underground with a walk behind vibratory plow.
I prefer the high amperage contactor (relay) near the pump approach in that you need only run a smaller gauge wire over the distance. Two-pole industrial contactors are readily available. My well pump is triggered by a pressure switch that is remotely located relative to my well pump. The pressure switch operates a simple
contactor providing electrical power to the pump.
There are "wireless relay options" available - not cheap, see http://migro.com/irrigation.htm.