I must say your whole computer design is quite strange, especially getting a 1000W PSU, which is complete overkill, and a non-reputable brand. But that aside, if the GPU is the element causing you problems it is not a systematic problem regarding all 560Tis, it's just yours. In which case send it back and get a replacement under warranty.
I do not think it's necessarily the problem causer though. Stress your CPU with some Prime95 torture testing, see if any crashes occur. If you're still stable I suggest you run a furmark burn-in cycle, and see if you start crashing again. The only problem with this is that it significantly stresses the CPU as well as the GPU.
It's much harder to tell between a faulty GPU and faulty PSU. I know OCCT has a power-supply test feature built in, but frankly I don't know how good it is, so if anyone here has more knowledge on OCCT PSU stress test feel free to provide it
Back onto OCCT - run their GPU memtest. Now this test IS buggy; sometimes it doesn't work well at all, but a large number of errors, combined with the issues you're experiencing could further indicate a manufacturing fault in the GPU.
All in all, if you're getting persistent issues when your GPU is stressed, and only when your GPU is stressed, get a replacement under warranty. If that doesn't fix your problems my second bet would be in the PSU.