So first off the hardest part: getting the remainder of the old hook out of the way. Sawing them off turned out to be the best solution with the tools at hand
Did some predrilling just to be safe and then got the hook screwed in a bit. The springs hold quite some tension, and getting the hook completely screwed in and hooking in the screw was a little too much. Instead, hooking in first and then screwing the hook all in worked great