I just finished replacing the x-clamps including completely cleaning and applying Arctic Silver 5. The original issue was overheating.

Now my Xbox will run for about 10 minutes flawlessly before the sound will suddenly stop with a loud beep-like noise thru the TV and the video will freeze. I can leave it like this forever and it will never give me red lights nor show any outstanding signs of any issues, overheating, etc - the video will just be there frozen without sound.

I expected eventually I'd get some red lights but never anything. Left it on for a long time and nothing.

I can restart it and immediately play for another 5-10 minutes~

Any idea what the issue may be?

HANA/ANA chip overheating or VPU RAM. I´m not sure though.

I think your solution is the heatgun! heatgun HANA/ANA chip and the connections to the GPU, also do the RAM chips. Good luck