I agree, all thread comes in very handy and you can add a slide hammer at the top to add upward pressure. Add washers, put it through a socket or whatever.

I am not quite clear either, but it sounds like the steel potion needs to go further in? If that is the case I found certain socket makes, in the size of about 13/16's seem to fit the head nice and tight. You could use one to tap the steel further in.