I elect not to answer your question.
Really, there are two questions: One in your title, "How do I setup my studio for shooting large rugs from the ceiling?" And the other, "Could you please suggest the best way for mounting the camera to the ceiling, ...".
What you ideally want
A flatbed scanner is what your ideal solution is. You have a planar surface that you want to capture in the most uniform lighting. Since that is what flatbed scanners were invented for, you'd want one of these. Problem, they don't exist that large. But remember, this is the ideal you strive for.
What you proposed
In your question you write that you have already decided on a camera, a lens, and a robotic camera mount.
- Lens: You want to use a 50mm lens on a crop-sensor camera? Indoors? I'd suggest you calculate how far away you can put your camera and figure out what lens would get you the appropriate part of the carpet into the image. Also, about that f/1.2: Especially if you are shooting at an angle at the rug, you will never use it at 1.2 because everything will be out of focus. But if you are shooting at f/5.6 or f/8, you could get a much cheaper 50mm 1.8 (if 50mm you really want).
- Camera: Why are you going for a high-end camera, when you don't need it? You should get the most basic one that still let's you control it via your GigaPan Panorama Head. My point is that in this instance you don't need fancy auto-focus, timelapse mode, high ISO, etc...
- That robotic panorama head... It would work and automate the process for you. There should also be no problem in mounting it to the ceiling using a Manfroto Arm or something a bit stronger. But think about the flatbed scanner... You want to take images as orthogonally to the rug-plane as possible.
You haven't mentioned lighting. That is the most important! It is not necessary difficult but I'd almost start with this.
- Get 3 of the cheapest Canon Camera with a 50mm 1.8 Lens, or other prime lens (this depends on the room you are in). Attach them to the ceiling using a Manfroto Arm or something else. Tape the focal lens. Build your own cable trigger. Transfer the images automatically (Wi-Fi SD card or something else) to a computer. Set up your required image transformations once (the cameras don't move!). Hugin, autopano would be two free, open-source solutions, but others including Photoshop work, too. Also, add cheap flashes, ideally you want very uniform lighting.
By the way, I am not proposing putting the camera next each other. I am proposing putting them at different positions of the ceiling so that each can shoot straight downward!
- A tilt-shift lens would work, too. But the downside is that you have to do this manually. Also, you don't get higher resolution.