I got just enough Goop in the housing to glue the barrel block in. Maybe 1/2 a drop, but it doesn't take much when the parts fit closely. Two whacks to the muzzle with a plastic mallet and I knocked the barrel assembly down into the housing. Then I clamped the barrel in my bench vise and twisted the housing back and forth a few times to make sure nothing else was sticking in there, and the housing slid right off. I wasn't worried about damaging the muzzle because the barrel has a recessed crown, and the stainless steel is a lot harder than the plastic mallet, which serves the same purpose as a rawhide mallet.
When I took a closer look at the muzzle I saw some carbon buildup, or something, at the muzzle and cleaned it up. When I put on my reading glasses it was easier to see that there was some damage to the muzzle. I don't have the proper tools to repair that kind of damage, but I do have a ceramic stick for honing knives. It has 4" of rod sticking out of a 2 1/4" wooden handle. So I poked it in on an angle and worked it in and out about an inch all the way around, being careful not to hit the bore on the opposite side. I kept going until it looked like a uniform chamfer, but I need to check it with a magnifying glass.
I'll be buying a .578"x28 die and die stock, and putting on an A2 flash hider I bought last year. Nothing will hit the muzzle after that, unless it's a cleaning rod. Other than the little speck of carbon, the barrel looked pretty clean when I swabbed the swarf out with a wet patch. I ran a brass or bronze brush though it anyway, then a wet patch came out really dirty. I don't know if I ever cleaned the brush, but I need to. Then I'll have to clean the bathroom sink.

I think the brush was putting crap in the barrel instead of taking it out.
I noticed that half of the screws for the housing looked like the heads had been hammered on. Then I remembered I did that to try to tighten up the opening of the sockets. They're 9/64" hex screws but a 9/64" hex wrench is a sloppy fit. Nothing else I have, SAE, metric, or Torx, fits any better either. So I put all 8 screws in the barrel clamp and hammered the other 4 down until they matched, then filed them down flat, 4 at a time. I'm going to run each one through a die to clean up the threads, then degrease, and paint them. And make sure the holes in the housing are all bored out to the same diameter, 5/16" I think, with no Goop or plastic handguard over the edges of the holes, and the bit goes straight through both sides.
Trivia time! I had to open a new package of patches to clean the bore. They're made by Southern Bloomer Mfg. Co. of Bristol, TN. If anyone isn't already aware, they started out making cotton knit panties and night shirts for state/federal mental institutions and prisons. Five years later they found that the scrap from this business made excellent gun cleaning patches. Their cotton knit products leave no strings or threads and are virtually lint free.
From prisoners' panties to patches.
https://southernbloomer.com/