+1 on the drive shaft u-joints. I had a nasty vibration acting similar to what you are describing and it was a u-joint. Block the wheels, put the T-case in neutral, get under it and play with the drive shafts looking for slop in the u-joints. Important that your t-case is in neutral so the shafts can move freely.

Can probably pick up a u-joint from a parts store for under $20. Wouldn't worry about the balancing unless you replace it and it still vibrates.

The leak is probably not related. I have the same leak with my 5-speed and no issues caused from it that I am aware of. Have not looked into where it's coming from, so if you figure it out anytime soon, post it up.

01 Convertible; Electric Fan; 3" Up Your Kia lift spacers; Tj 104's; 31x10.5x15's on Centerlines; Rear LSD.
GONE, all I have left are a few spare parts and the wheels.