You're not going about this the wrong way. Systematic troubleshooting is really the only way to find a problem like this. One thing that you could also try is to run memtest86 to see if there are any errors.
If you think that you might be overloading the PSU or that the 12V rail for your EPS 8pin may be bad then you could use both PSU's in combination. One you use the 24 pin and the other you jump it with a paperclip (google for a diagram of what pins to jump). Turn on the jumped one first and then power on the computer normally. They will share the load.
If you know anyone else with a computer then that would be a good way to test the video card. Ask them to let you try it in their system to see if it will work on its own.
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