The shims will definitely help take the slack/play out. Stack them if needed to make it tight.
That said, I fought the wings for a couple hours because they would not slide on easily with the thicker ultra high-clearance hitch crossmember. What finally worked for me was lightly sanding all the contact points, then applying a thin coat of grease to the mating surfaces. After that, the wings slid on with a lot of pushing and grunting. I don’t have room to run any shims it’s that tight but everything is lined up after some persuasion.
I will note that there is a method of installing the wings by tilting forward and sliding in, which allows the forward part of the wing to clear the front wing stiffener. My hangup was on the outer corners of the thicker ultra high crossmember.
