So looking more at the WNMHGB bridge, it seems that it's a little more complicated.
If I use the main viewer as the reference point for being forward centerline, then the turbolift position didn't change between The Cage and S1. The helm station and Captain chair just happen to be rotated to their right 18 degrees.
If I use the Captain's chair and Helm station are the basis for the forward facing, the turbolift is moved closer to centerline by 18 degrees and the main viewer is moved off centerline by 18 degrees to their left.
Interestingly, it appears to be very deliberate as the forward left railing is shorter in length to accommodate the more "compressed" port side of the bridge. Since we don't see parts of the forward starboard bridge, perhaps extra equipment was installed their for their extra-galactic mission pushing everything to the portside?