I run a bunch of Corsair 1000's and have not any any issues with them. I don't push them as hard as you though, and I keep them to a maximum of 800-850 watts on input, meaning they are probably delivering 750-800 output. I also run them at 240V input, so this is a little easier on them as the input current is slightly less and PSU efficiency is slightly better.

For the OP pushing the input over 1040 watts and 950 output, while you may technically be within specifications, I think consumer PSUs are designed more for the 1000 watts to be a maximum surge current, and not a 24/7 constant load. I would look at reducing the load on it if you expect it to last and to also minimize fire risks.