When you run the unigine heaven benchmark and put your head near the PSU at the back of the case, can you tell if it's loud or not?
Can you also make a video with your case closed while running a benchmark? I mean based on the benchmarks this card should be extremely quiet and based on your fan speeds and temperature readings, it's barely even breaking a sweat. I mean if I took a video and put my smartphone right next to the GPU, it would also be loud since you are zooming in 1 inch to the card but sitting away probably 1 meter from the desktop tower. Your card sounds loud up close but is it loud in the case? Those temperatures of 61*C look amazing. Lower the GPU fan speeds to 10-20% manually in MSI after-burner at idle and see if the card is loud, then start raising GPU fan speeds in idle from 20% to 30% to 40% to 50%, etc. See at which fan speed the card becomes too loud for you.
What specific model of GTX560Ti did you have before btw? Just trying to figure out if your card is very loud, or you are just extremely sensitive to noise levels and the video you made just sounds super loud because the phone was so close to the card or the card's fans are faulty?
Also, you still haven't said if you specifically listened to the PSU under full load. I kinda want to isolate that the PSU is not the loud component so I need you to get down to the PSU level at the bottom of the case and put your ear right next to it where the vent holes are at the back of the PSU when you are running the GPU at 99% in that benchmark.
The other thing you should do is when the GPU is running, use a finger in the middle of each GPU fan and push slightly on each fan to stop it. Do it for the left fan and see if the GPU got quieter, then quickly release the finger, and do it for the 2nd fan. Maybe one of those fans has a faulty bearing.