I used this strategy to get my last 7 or 8 cards.
I just got 4x each card last night. It took me 43 games to get my last card - Ormec Head (makes me think of Cormac62, my old nemesis).
I changed the map to Bisteam Forest thinking that more Earth cards would be given away there. 20 cards are awarded to 1st place on Dark Abyss - only 17 on Bisteam Forest. I figured just like in Saga, the elemental maps would award more cards of the matching element. I'm not sure if this theory is correct, but it did only took me three games played there to get my last Ormec Head.
When I got my 4th Nuclear Fusion, I had 6499 total cards and only needed one more Ormec head. When I got 4x all, I was at the 7350 card mark!
Thanks again for sharing your idea Monk!