Okay, I don't know enough about what I'm doing to understand all the possibilities, but I found something that might help. I made a box in Wings, and I UV mapped it so that the sides and bottom were outside the grid, and the top went corner to corner. I imported it into Carrara (with the check box for "Assume UV's in range 0 to 1 off), and mapped a copy of your kitchen floor image onto it. I got a duplicate of your results.

I went in to the Model Room, selected the entire object, and clicked the UV map mode. I changed the mapping to "Box Face" and just for fun, clicked "Top". That rendered correctly.

When I first looked at the custom UV's, they didn't match the UV layout I had in Wings.

I have no idea of this is a Carrara problem, a Wings problem, or a problem with my inexperience, but I strongly suspect the latter.