I am a guild master and run Kara with my guild, but I sure wish it would reset more often so I could try some fun things.
I would be willing to bet post-nerf that you could have just a reasonably geared group consisting of:
1 Prot Paladin
2 Ret Paladins
2 Holy Paladins
and you could probably 5-man the place. I don't even think you would need anything above Kara purples with even a few blues. I know of T6 geared groups that 4-man the place now. If you wanted to make sure you were safe, you could bring another Prot or another Ret and 6-man it.
I would just LOVE to be able to try this and have a Pally-fest in there, but my guild would frown on their leader/main tank skipping a weekly guild run just to mess around in there :)