I don't think this is a power problem as he says it does same with one card and Claymore just starts and then shuts down without him being able to see why.
Open CMD prompt as administrator
Navigate to the Claymore Folder yourself
Copy your long Bat file command and then paste it into the cmd window and press enter.
This way you will be able to see the exact error Claymore is giving.

I have seen this type of crashing in the past when it is missing some sort of DLL file or something. Installing VB.Net or Visual Studio usually sorts this out.
Also maybe you can post your Claymore Log file?

But yes, if you are not going to undervolt that 1200W PSU might be a little bit too small for those 6 Cards! With proper undervolting it wil be fine though.