Brickyee,
I described the custom replacement barrel and cutters, too, but they don't produce continuous contact when tight link holes are employed. That's because the cutting is straight into the link lugs rather than along the arc the pivoting link describes, and also because the leading (front) edges of even the oversize replacement barrels are cut not to jam a minimum size link. Only with enough play in the linkage will those surfaces make pin contact rather than the link riding the pin. The old weld-up method allows the lugs to be shaped so the arc of the link is followed from battery to counter-battery. I can't say that seems entirely necessary to do, but it does eliminate impact of the lugs on the pin as the slide starts forward, and that is good for lug and pin wear.
You can take a modern replacement barrel with extra metal and use high spot die to scrape it in as far as it allows rather than using the cutter. It is more time consuming. Using the undersized cutter Brownell sells, followed by hand scraping only the last bit seems to me to be a good compromise, but others may work differently.
Dahermit:
You were correct that the old barrel had a timing problem. It is pretty much standard practice to take a triangular scraper and break the edges of the locking lug recesses in the slide and on the barrel because sharp edges can interfere slightly on an otherwise correctly fit barrel. Obviously, an over-long link can drive the barrel up against the bottom of the locking lug recesses. That usually ends up undoing slide-frame fitting by gradually prying it open. But when there is interference beyond that, and a bad case of locking lug edge battering with any length link, the barrel extension (hood) is likely too long and the breech face of the slide is starting the barrel forward ahead of reaching position to align the slide's lug mating recesses. Usual practice on a match gun is to set about 0.002" clearance at the back of the hood. That lets the barrel's forward movement lag the fit position very slightly and makes room for a little bounce before contact between the slide stop pin and link lugs occurs.
By they way, you don't need a lot of locking surface interleave, as the looseness of the original tolerances demonstrate. David Chow used to use a small piece of spring steel jammed up into the rear lug of the slide as a way to tighten barrel-to-slide fit rather than necessarily having to increasing barrel link lug height and the length of the link. Fred Kart's
Easy-Fit barrels accomplish the same thing working from the barrel side. They have a couple of filler bridges (pads) in the rear lugs that are upward stops. You file them down just until lock-up is tight. They work just fine.