If you know people, I'd make a full party and farm that way. It's faster, and you can work out terms and stuff with them, rather than randoms that are like, "LOL, MINE."
I honestly don't think rank plays a role in the end-dungeon reward cards. I believe the highest factor in those are how many Champion monsters you've killed in the dungeon, meaning full runs might give a higher chance, though the fatigue ratio and time it takes probably isn't worth it.
Oh, while we're on this topic, if you have a full party, you could have a higher chance of getting the rare end-dungeon reward card, since you can have your friends ALL buy the premiums. A friend of mine suggested that if there's more 0 Rewards at the bottom, it means there's probably a high chance of one of the other cards being a rare.
If you're ever trying to farm for Bamboo Bracelets, let me in, lol. I need one for my Battle Mage.