And it's done. After about 12 hours of winding, cutting, linking, screwing the pattern up, taking it apart, and linking again, here it is:
I think it came out ok - it looks a little squashed, but that's more a limitation of the 4-in-1 weave I use, as it can only do 45 degree slopes rather than the roughly 60 degree angles on the logo. Also, the purple stars aren't showing as much as I hoped they were - I'll have to do another version with a purple backing and silver stars to see if the contrast works a little better.
On the plus side, it turns out I horribly overestimated how much wire I would need and got twice as much as required, so I can make smaller versions and mount them as patches on the sleeves of my 16-gauge steel mail shirt - the aluminum just doesn't have the strength to hold the entire weight of the steel, so putting a single large inlay on the front of the shirt will simply result in it pulling apart under the weight over time. Hopefully the 3/4 length sleeves I plan to make won't be heavy enough to do any damage.