[David Swanson]

If my After Effects weren’t spending over an hour analyzing in the background I’d test this idea out. I’ll explain it as organized as I can, so the following should be seen as a hierarchy of compositions and layers:

The Master composition would contain a pre-comp (name the pre-comp “Offsetter”). That pre-comp will be as big as the Master composition. You’ll add the offset effect to the pre-comp (just like you’ve been advised to do previously). Animate the offset to your hearts desire.

Before you make the Master comp, you’ll need to make that Offsetter composition (this is why we read instructions before applying the solution). Again, make the Offsetter composition the same size as your final output (whatever Master comp will be). The only layer you’ll have in this Offsetter composition is it’s own pre-comp that will be called “Rotator” (or whatever you prefer). The Rotator pre-comp will be smaller than the Offsetter composition (however small the object is in comparison to the final output size). The Rotator pre-comp will be dead-center in your Offsetter composition and the object within the pre-comp will rotate (if you were to ram-preview it). There’s nothing more that you need to do with the Offset composition.

Before you make the Offset composition you need to make the Rotator composition. That composition will be slightly larger than your object (this way it doesn’t get clipped when you rotate it). Dead center of the composition will be the object you intend to animate. Animate that object (rotate or whatever you want), and that’s all you have to do with this composition.

All of this should work and the only reason it might not is because I don’t know if offset will treat pre-compositions the same way it would treat footage or graphical files. If offset doesn’t work on pre-comps then render the Offsetter composition (include alpha channel) then bring back in and repeat the previous instructions from Dave.