As far as Constellation goes, it depends on whose model you're lookin' at.
Oh, I agree completely, Guv. Let me show you the model I'm using:
This is the actual studio model of the USS
Hathaway, redressed for exhibition as the USS
Valkyrie. In the picture below you can still see her old name under 'Valkyrie":
So, in the blue box of the pic below we have the original officers' lounge construction, but with the bridge module replaced with be back-to-front tactical sensor array.
Now, the fun part is in the red box! Here's another angle below, but less clear:
Now, doesn't the contents of those red and white boxes look like a resin cast of a Constitution photon deck to you, top and bottom?
It may not be lit up like a photon tube in the eps, but that's the part it was made from. And since the exhaust ports of the twin impulse engines also weren't lit up during the eps but are clearly Constitution/Miranda impulse engines...
My Connie has two photon decks for 4 forward tubes. (I originally gave her two Excelsior-style "hidden" photon tubes at the front of the saucer, but these pics and the cutaway from the Star Trek Magazine dismiss the need of them.
On another note, I have done some non-canon pics of the "original"
Scorpio with a proper sensor array (see below), but I really like Mohab's suggestion that it is a faired-in captain's yacht.
I also did a version of this with some photon tubes, but it's not canon, and I actually think the photon bridge spoils her sleek looks. Tell me what you think: