Here is another mock-up as far as the general gist of my direction:

Now I'm not saying you would necessarily see the "Piett door", much less have it OPEN when Vader is talking to the Emperor... but the mock-up (as sloppy as it is) is to create the overall impression of what could be done to indicate the meditation room as connected to the holo room.

I guess a couple of points to bring up too:

(1) will the holo room walls be toned to grey to match the meditation room wall colors?
(2) will there be anything coming out of the "red lights" on the posts to indicate the hologram projector(s) (nothing as harsh as say when R2 projects a hologram, but maybe have the red lights turn brighter blue and flicker a bit - even if there is no hint of a projector beam - just to show that the holo-room is on and active).

I can also understand if any of that (regarding the hologram projector beams/lights) would cause distraction, as the main point of the scene is the conversation not the FX.

Angel: actually, I was the one who offered the elevator idea. Here is my mock-up (I think it was me.. maybe we had the same idea... damn old age):

Frankly, this would be the simplest thing to do, as it could place the room anywhere on the Executor (far away or near the bridge), give Vader an airlock/privacy and wouldn't involve creating any extensive FX work (okay, a TON of FX work).

The door behind Piett could be shown closing as the doorway he is in now opens, or there could be a slight lag whereupon the white light panels on either side of Piett give a slight glow of red and turn green.. then the doors open and Piett comes in (indicating the airlock is sealed on the other side and/or Piett has been decontaminated).