Since you seem to be very good at analyzing photos.....Here's the deal.... I don't believe that the rifle in the photo was actually there.
1st off ---I believe the photo was taken at night..... The rifle was discovered at 1:22pm and the in situ photo was allegedly taken before 1:45pm , so the area should be bathed in bright sunshine from the window that was in the west wall.
2nd --- If the photo was taken at night then the carcano wouldn't have been available , because the FBI took custody of it. and it was in Wash DC
3rd--- The stock on the rifle does not look like the stock of a carcano but the muzzle does look like a carcano.
I wonder if they could have used a mauser ( the stock looks like a mauser) to take the photo and then altered the photo by placing the photo of the muzzle of a carcano ( we know they had many photos of the carcano.) on the photo.
1) The shadows in the photo are very pronounced and were not created from the camera flash. The light source came from the right of frame either from the sun or lighting on the 6th floor. If you had a surveyed overhead image of the TSBD (Google Maps) and knew the layout of the 6th floor relative to North, and knew the sun angle at 1:45pm on that fateful day (which any astronomy program can give you) then you could tell whether the shadows contradict the timeline. But that's way too much work, and who would believe you? But fill your boots.
2) Yes, unless the rifle was photographed when the DPD claims they are busted..again, just add it to the plethora of other shenanigans they were up to. How come Alyea wasn't allowed to film the rifle in situ? Because Fritz called the shots.
3) I agree that the stock does not match the MC but the forend definitely matches the MC. If you rotate the rifle Day is holding up ~90 degrees along its axis so it is perpendicular to the floor, it's a perfect match, which includes the 2 screws.

However, I couldn't make the rifles match over their entire length when I scaled the forends to match. I couldn't attribute the discrepancies to a simple rotation or foreshortening.
You should be able to settle this by setting your MC down in a similar orientation and take some pics from the same POV and compare the images. You should be able to either match the in situ photo exactly or the gun is smoking. Then you could answer all your own questions. That is unless you don't actually have a MC. Then I would understand your reluctance.
Considering how Fritz controlled the crime scene and exactly how it got documented, including staging an in situ photo of the 3 hulls, which he removed from his pocket and tossed onto the floor in the sniper's nest and had a rookie cop take the photo, I wouldn't doubt that the photo of the MC ditched neatly beside the box is just more Fritz bullshite. Add it to the list. Otherwise, I'm done with this one until you post your re-enactment photo with your MC.
Good luck!