Easier to Take It Off . . .
. . . Than to put back on whatever was taken off in the first place.
It seems to me that JohnHL and you were/are on the proper tack: You've got a larger-than-usual gap in ye olde inspection port and a hang on the barrel's extraction, so take a little out of one end to get a proper function in both ends.
For whatever reason, it further seems a previous owner got a another, new-to-that gun barrel for that 5944, figuring it'd just drop in and all would be well.
Given my personal experiences with use of both a Dremel and some Arkansas stones, both have their place.
The stones are the more forgiving. The Dremel can flat out ruin a day in nothing flat. Given what I ruined, taking my time with a stone/s has proven its value many, many times over to me. Plus, there's a keen sense of satisfaction when whatever I've worked eventually drops perfectly into wherever it needs to go.
There's one last thought that deviates slightly from the above.
It might behoove to check the barrel's round where it meets the bushing as well as that of the up-front bushing.
Also, it would not surprised me to find your barrel "juts" from the front of that bushing just about the same distance as one might need to shave from the barrel's rear.
These are among the vagaries experienced when purchasing a used firearm. We who do so have no idea what transpired previously and must tread carefully.
While I did not expect to learn so many, many things about my firearms going into it all, I am glad for the learning experiences that have since transpired.
In the end, should a used-gun buyer not wish to tread where he or she has not desired, find an excellent gunsmith (most are easy to find today; they're gray hairs) and be willing to shell out a few extra bucks for his knowledge - no doubt gained through a few screw-ups, too.
It's like that time I decided my 318 Dodge engine's valve train was going a klackety klack too doggone much. So off came the valve covers and on went a properly sized socket. I cranked that klackety right out of those suckers. Every doggone one.
And on the very next crank that 318 didn't run worth didley squat, on top of it darn near shakin' itself out of my Polaris 500's engine bay.
The next day I learned about engine lash and that a properly lashed 318 valve train tended to go klackety klack. A lesson that cost a few bucks and a good deal of embarrassment, too.
Later.
DC