Putting a 2.5 inch in a 3 inch hole? I can see where a sleeve would add extra play. And that play is like a hammer on the pin. (Short stroke, but it is a big hammer)
If it was mine I would cut some 1/4 inch mild steel to match the size of the 4 sides. Drill a couple holes in a pair of them, where I'm sure the pin hole will not be. Line 1 up, and tack thru the holes. Then I would use the 2 holes, to drill thru that plate. Repeat for other side. Tack top and bottom on, check for fit. Then using short welds, to keep from heating it to much. Grind a little taper on sides and bottom just to make it easier to start in.
Now I have faith my welds will not break, or cause the stinger to bend/break. But unless enough breaks for the top/bottom pieces fall out, you are no worse than now.