The reason carpet guys only cut X's in the carpet is because we let them. If you had the opportunity to run all of your conduit and cabling in the ceiling unsupported, and then said it's the ceiling guy's responsibility, don't you think most would try to get away with it. Just as there are times when we have to get cut sheets for fixtures, equipment and gear, let the floor guys get a cut sheet for the proper trimming of carpet or flooring. Why should we have to do other trades' work? I would tell the GC "why would I tell the guy to cut to the cover when I know better? It's a shame that he isn't bright enough to figure his own "trade" out, but that's not my problem." I would help resolve the problem, but would be getting paid to do so, or the carpet guy can install new carpet.
Sparky, you are not at fault one bit.