Just one more update here for those that are interested....I removed the original receiver from the truck with the help of a welder friend who has a plasma cutter, and welded the new tighter fitting one in place. The original had .120" clearance between it and the Reese hitch, and the new one has .060" clearance, so I figured a .060" shim would work, but I was wrong. To get it to fit, I had to mill it down to .055", and now it works. Not as easy to install and remove as before, but OK.
I have also towed with it for a few hundred miles, and it's better than before I started this "experiment", but not as good as when the set screws were tight.
In the future, I may install set screws on this one, change to a solid hitch insert, and that would do the trick, I think.