Shawn,
Mine has the same slop in the fine adjustment. And that's what I remember of the one's from 40 something years ago. I took mine apart, the pivot pin is a straight pin about .105" in diameter. It's not tapered. I might change that if I have any tapered pins that small. I have reamers, that's not a problem. I also measured the width of the slot and the thickness of the tongue. The slot was .129" wide at the bottom and about .125" at the top where the knuckle joint attaches. The tongue measured .120" the full length. So there is definitely a slop problem.
I would make a brass shim to place in there to take up some of the slop. I don't think you will eliminate all of it. The shim will just make it a little better.