You had the Inquisitor set and a spare Nano mod? Don't get me wrong; I can sympathize with your frustration, but that's an impressive collection to just throw away! :o Incidentally, if you don't successfully pick up DS, there's a chance it will spawn again later. (I once had it spawn three times in the same ArchAo666 game!) In previous versions, you got credit for finding DS by *trying* to pick it up, even if you weren't successful. (That's how I got Armorer Diamond in the earlier version) In this version, you don't get credit unless you successfully wield it, so Armorer Gold and Diamond are impossible badges unless you discover the secret.
Easiest Diamond? Yeah, probably Technician, since you don't need any particular skill except to play lots. Other than that, I think it depends on your playstyle. I think Shotgunnery is pretty easy, but that might just be a reflection of the fact that I like the shotgun. UAC Diamond (the speedrun one) might be easyish in that you can just do a stair-dive and hope you get lucky. (it will probably take you a few dozen tries, but hey, they're speedruns, so they'll be quick) :) I hear that Gatekeeper Diamond is fairly easy, as long as you get the right traits (ie Dodgemaster) and are careful when it counts.
And yes, Angelic badges are unlocked when you get your first Diamond.