I would suggest you to remove the lock from the carrier. You can return the part and get your money back. You'll be using your jack hook to rotate the carrier.
To remove the lock, you can pry out the cone shaped plastic first (it'll be right around the lock). Once the plastic is removed, you'll have a bit more access to the lock. With some persuasion you might be able to pull out the lock without breaking the outer cone shaped metal. Just take your time.
The lock looks like this once removed. Only thing that's keeping the lock in the carrier assembly are the washer with many teeth. When I was removing my lock, I thought the cross pin looked like something removable. I ended up destroying the outer metal.
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It's OK if you end up removing the outer metal cone. The cone can be helpful to guide the jack hook to the right position, but you can still operate the carrier without a lot of problems. My carrier looks like this now.
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