Hey there!
The amount of work it takes is.. Not that much, you can just do 7 random cataclysm dungeons as a tank, transfer, and do 7 more. That should be enough for nearly all Justice Points gear. I'll show you my
resto druid which I geared in 2 days, you can see that I really only have JP gear + some craftables/BoE trinkets. The ICC 5 man heroic weapons are suggested though, but not hard to come by either. You can get every single piece of gear epic (200-226 ilvl) just from the Justice Points vendor (bar one tank trinket)
You will certainly be able to finish your set before saturday night, if you have some dedication.