I get the sense that you are new to the details of photography, so here are a few basic points.
Your prior camera, the 600D, was a crop-sensor camera using the EF-S mount. This sensor was smaller than the full-frame sensor in the 5D series cameras (and the 6D and 1D), using the EF mount. So, the 18mm wide end of your EF-S zoom lens on the 600D is actually equivalent to a 28mm EF lens on a full-frame camera.
There are a number of EF lenses that cover this range. For primes, you could look at any of the 28mm lenses. If you are shooting handheld from a ladder, you might consider the new 28mm f/2.8 IS lens, with image stablization that will help with any blur from handholding. There is also a 20mm f/2.8 lens with a wider field of view that is inexpensive. For zooms, there is a 17-40 f/4 and a 16-35 f/2.8 that would probably work as well. Zooms generally have smaller apertures, so they require more light, but that should not be a problem with a 5d mark 3 or 6D (although the 5d mark 2 it may be). For wider apertures (1.8, 1.4, 1.2), note that the field of view, or the area in focus, is very narrow. For more detail, you want smaller apertures (larger numbers, like 5.6, 8, 11, etc).
The TS-E lenses are manual focus, and would require you use a tripod and spend lots of time with them. The "stitching" of images is also more time spent on the computer afterwards. It does not sound like that is what you are looking for.
However, changing lenses is not hard or time consuming, and you could also get a 100mm f/2.8 macro lens (the version with the IS if you are shooting handheld) to take your detail shots right after you take your wide shots. Or you could get the EF-S 60mm macro lens and put it on your old 600D for your macro shots, but note that this lens will not work on your new full frame 5D.
Also, you should look into the 6D camera. Its built-in wifi might be useful in your working environment, and the autofocus will be plenty for photographing stationary carpets. The images should look just about as good as the 5d Mark 3, and maybe even better than the 5d mark 2. (This is the kind of thing that people on the internet argue about a lot, though).
I hope this helps.