Can I swap the RadeonHD 6770M GPU to new logic board?

iMac (2.7GHz) is not powering up and Apple ruled out the PSU and suspects the logic board. I looked into replacing it myself, but have discovered that the replacement boards are not sold with the integrated RadeonHD 6770M. Is there any way to swap the GPU from the bad logic board onto a new one?

Looks insurmountable to me, but curious if anyone has tried it. I've seen the step-by-steps for GPU replacement on the same board, but I've no idea how I could remove the GPU and secure it to a new board.