How do I install an in-wall tank (wall-hung toilet) with the stack in the way?
The simple answer to your dilemma is that you have two choices..either relocate the toilet location to one side of the vent stack - or - to route the vent stack pipe around the place the 'in-wall' components are mounted. 

On top of that if your stud spacing is not now 25-3/8" you may be doing some framing work in your wall anyway.