I do not know if the correction should really be to turned off (in practical calculations) for the rest of the system, which is not a layered stack. But that might work, since the dispersion forces are usually essential only for the layered stack when it comes to geometry optimization. Actually, it also depends on the system, since there are 3D materials (e.g., some oxides as far as I remember) where the van der Waals forces are important as well.
Regarding setting the vacuum thickness, it is pretty much up to you, as there is no chemical interaction between the metal regions and the actual atomic structure - it is pure electrostatics determined by the Poisson solver with particular boundary conditions imposed on the metallic regions. Your system looks like Dirichlet (or Neumann) boundary|vacuum|Stack|vacuum| Dirichlet (or Neumann) boundary, where the two vacuum regions act as dielectric spacers (with epsilon=1) in which the electric field will be constant.