Just to make it clear, all work needs to be done on the barrel, never make any changes to the frame or your other barrels won't fit proper.
You can make a temporary shim to wrap the pivot pin to find out how thick the shim needs to be to get the barrel tight at the standing breech. The goal is to have no visible space at that point, and a .002" feeler gauge blade placed across the breech above the firing pin should be real tough or can't be pulled out of the space there...while a .001" blade can be pulled out with some effort. These 2 "specs" are what a factory fitted barrel will yield. I use sode pop can material for the temporary shim, it usually measures .002" and you can use multiple layers to get a thicker shim. Once you have determined the right thickness, buy a cheap feeler gauge set at an auto supply store, look for a set that has .001" increments in the blade assortment. Choose the right size blade, anneal it by heating it cherry red then let it air cool. Cut it to the width of the barrel lug pivot then file the piece so the edges are nice and flat. Rough up one side of it so epoxy will adhere good. Clean it and the barrel pivot well with acetone or alchohol. You'll also need something that is the same diameter or slightly smaller than the pivot pin which is .370" in diameter. I have a brass drift that is .368" that I use to press the shim into the pivot using a "C" clamp. Just place the shim against the pivot surface, place the round drill bit or whatever you use against the shim, place the clamp jaw against the round stock and the other screw end of the clamp against the edge of the latch shelf and tighten the clamp. This will force the shim into the pivot surface and form it to the pivot. Once it's formed, just mix up some JB Weld epoxy and epoxy it together. Make sure you use a release agent on the round piece so you don't epoxy it to the barrel. I used TC Bore Butter on mine because it was handy, but Pam or just about any oil or grease should work, just be sure not to get the release agent on the epoxied surface or the epoxy won't hold. Wipe away any excess epoxy from the underlug surface and let it cure. I used the 4 minute JB Weld and it is fully cured in 4hrs at room temp. After it's cured used an 11/32" drill bit wrapped with emery cloth to make the final fitting. You want the emery cloth wrapped drill bit to measure as close to .370" diameter so the pivot surface is the same size as the pivot pin...so use the right size drill bit to get that total diameter including the emery cloth. After you get lock up and the correct spacing checks are made, work on the latch shelf according to the instruction in my other post. Once you get everything fitted correctly, apply a bit of grease or oil to the pivot pin, I use Tetra grease on mine, but any lube will help maintain the tolerance of the fit so the barrel doesn't loosen over time. The latch and latch shelf should be dry, no oil there, just a smooth surface.
Good luck and ask questions if you have em!
Tim