Apple's engineers did the worse possible setup here! It's not easy for sure. The spring doesn't need to be as powerful as it is. I carefully bend back to spring tension so it's easier to set.
I find a tongue depressor can help, I cut it in half so it can go across the top of the chip along the edge on each side so when I pull them out the TIM gets squeezed where they where. Thus it holds the chip in the correct alignment within the socket. It's best to have a second pair of hands here.
Then how you tighten the screws is important! Just like how the lugs of a tire is tightened you need to ease the heatsink down evenly going in a cross pattern.