Reporting back with my fix for anyone else who has this issue in the future. As mentioned above, the size for these three accessory bracket mounting screws is something between an M3 and M2, which is problematic as it doesn't match any other screws in the chassis and it's not a size you're likely to have laying around. It also isn't threaded for any standard 'computer case' screws you might have. It's a mystery size for sure.
Anyway, my fix as it turns out was to run an M3 tap through them. The existing holes are sized very nicely for this as-is so you don't need to drill them first. The new threads took perfectly, and now I can use any M3 screws and the bracket is more solidly connected than it ever was before. Cheers.