Don't like the idea of welding a bolt to the sheet metal. Thick piece to a thin piece makes you blow thru which is NOT GOOD in this case. ..... and NO ACCESS to fix with a copper backing.
I think the eye bolt into bottom hinge thread is the best bet first. Use a slide hammer. You can control the hits. Pull up and out? Not sure. Just see what the metal wants to do and reset to a different method. Your first step is an information step. Very important!!!! Ease into this and see how the Z reacts. Don't apply any heat on it yet either.
I did think of a hole as Kevin says but thought that is one of the nuclear options. But plenty doable, but again if blow thru like I do, it's a mess. If you are a good welder of thin sheet metal that's different. Not many folks are. I am still not great at it and have done quite a bit. The problem is I do it then not again for years when a new project happens.
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