Yikes!. That link just looks so much like a 1911 my brain switched to 1911 autopilot with that kit recommendation. Also, now I look a little further into the parts places, I don't see Star links listed anywhere as separate parts. The Numrich schematic doesn't number them or the pins separately, but rather shows them as part of the barrel assembly. I also notice from DMK's photos that the metal finishing marks match clear across the pin. That and the lack of available replacements makes me think that link may be matched to the barrel at the factory and is meant to be permanent.
A couple of things come to mind. First, you might get away with just breaking the edges on the barrel locking lugs and recesses. This would mean taking a sharp triangle file and putting a very slight 45° chamfer on the edges of the barrel locking lugs and using a scraper (a small triangle file with the teeth ground off to form a sharp edge) to put them on the edges of the lug recesses in the slide. These might only need to be a couple hundredths of an inch across. Just enough to spoil the catch of the edges you feel now.
If that doesn't cut it, take a caliper and measure from the center of the link pin to the center of the assembly pin hole. See if that looks like .278". Measure the thickness of the link and of the assemble pin. See if you can push the link pin out of the link lugs and measure it. These bits of information will tell us how close 1911 lugs match the Star.
I've always made and heat treated my own links to get a perfect match to freshly cut link lugs, so this is possible to do as a last resort. But let's not try to have you go that far at the outset.
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