So, after delaying the job, I thought I’d try another method.
I zip tied the lock so it was out of the way, and to avoid hurting my fingers, I just used a long nose plier to get the short end behind the little plastic part.
The only issue I have is I’m finding that the pin hole is not aligning at all. I can, however, manually align this myself if I adjust the plastic hook. I wonder if this is normal or that I’ve done something wrong.