Okay, here's what my findings have concluded on the differences between the viewscreen on the TMP examination room set versus the viewscreen on the TWOK set. We discussed this in my older thread way back when, but figured it would be helpful to those that weren't around the first time, or don't remember
Here, in TMP, we see that the viewscreen is nested in a larger curved wall with those extruded rectangles running down either side. The viewscreen fills in the space between the gap in the wall, up until the "lip" at the top edge of the screen. Above this lip are more extruded rectangles.

We see that the viewscreen follows the curvature of the wall that it's nested inside. This is evident by viewing the top two corners of the screen. Notice the slight curvature. This curvature is actually more extreme than it appears due to the field of view of the camera and the fact that it's looking straight at the screen.

In this behind the scenes photo, we see that the wall above the screen also follows the curvature of the wall it's nested inside, and that there are at least 14 rows of those extruded rectangles above the screen.
Now then. In TWOK, this screen is different. The screen itself is nested in
another wall, this wall being planar and
not following the curvature of the of the main wall. This is evident by the drop shadow of the main wall onto the viewscreen wall. The "lip" remians, however. We can see that surrounding the edge of the viewscreen, there is a "frame" around it.

I am convinced that this viewscreen was lifted from Kirk's TMP quarters set, and indeed, it's dimensions match and so do the amount of squares going across the transparent panels of both (I counted

). And it has the same "frame" around the viewscreen. Since this wall was replaced in Kirk's cabin by a new wall, we can assume that for whatever reason, the TMP viewscreen of Kirk's cabin was moved to the sickbay set between movies. Also note that there are no extruded rectangle greebles above the TWOK screen.
We even see evidence of this in this behind the scene's photo, which would suggest that they hadn't even bothered to finish painting the wall to match the white of the sickbay set:
This deleted scene image, however, throws a wrench in my findings:

We see that the extruded rectangles are back, and they appear to follow the curvature of the outer main wall.
I surmise that the two scenes we have in TWOK (Preston's death and the deleted Checkov scene) were filmed on different days. Who knows which came first, but in the Checkov scene, we still have the Kirk's TMP cabin viewscreen wall, but the existing curved wall with extruded rectangles above it. I think that the TMP examination room view screen was removed, the curved wall above it remained. They wheeled Kirk's TMP cabin viewscreen wall in to fill the hole left by the TMP exam room screen's absence. AND THEN, for whatever reason, between the filming of the two TWOK exam room scenes, the curved wall above it was removed, along with the greebles. Maybe to get additional lights in, or maybe it was simply a flimsy piece of set that fell down or was damaged during filming/handling. Who knows?
Anyhow, for my TWOK version of the set, I'll be going with what we see in the Peter Preston death scene. I have, however, added an additional curvature above the viewscreen so that it meets nicely back with the upper portion of the main wall, rather than have it meet at a sharp angle.
These images may help show the differences a little better:
