I accidentally accepted this contract too, before discovering how hard it was to get off Eve. Although mine only required 1200 ore.
Can confirm that this "cheat" method does work:
Send two ships A & B:
Ship A goes to mine ore on Eve into a tank big enough for what ever the contract says.
Ship B launches from Kerbin, to Gilly, carrying enough ore that you load up while in the VAB.
Eventually when Ship A has accumulated enough ore, you can open the contracts window, and see the little green ticks, and the only one not yet fulfilled is the one about having the ore in orbit around Gilly (or landed on Gilly), so you switch to Ship B, which is already in orbit (or landed, whatever the contract says), then open the contracts window, and you will see the little green ticks all light up.