Honestly, I think the thing that makes it awkward is that they know you as an individual now. You've socialized with them as a couple; with her separately; together as a couple.
Even if you'd been, say, the sister of one of the people in Couples A and B and you'd got to know them all as much as you had, it would have been rude in those circumstances to hand the invitations out in front of you. It may have been easier to explain not being invited to the wedding as a numbers thing, having only known you as a sibling of a good friend, and it would have been easier to a accept too.
But as the girlfriend of a year's standing, someone they know well enough to ask favours of and choose to spend time with, this is pretty awful behaviour.
If no invitation is forthcoming, I would maintain a frosty relationship with them for the sake of my bf. Over time, I'd probably stop seeing them, let him see them alone. That's if I intended to stay with my bf.
As I've typed this I've remembered that this very thing happened to me some 15 years ago, minus the part about the couple relocating. My then bf was the last bachelor of the group, they were all a fair bit older than me (I was mid-20s, they were all late 30s-early 40s). They were late to marry, but they'd all known each other since university. It was pretty incestuous too: they'd all dated each other at some point or another before pairing off for good (well, turns out all but one couple are now divorced, but that's incidental). I didn't know any of this at the time, so I was forever putting my foot in it (bf was hopeless). One couple got married and invited me, even though I'd only been dating bf for a year or so, and it was plain for everyone to see that we weren't going to last the distance. Really lovely wedding too, lots of fun. Another couple got married and the woman was, basically, an older version of me. Don't want to sound catty but she was physically older, jaded, weary. Bf told me the reason she so bitchily didn't invite me (bitchily because her fiancé wanted my bf to have his gf there, for his sake, and she stopped him) is because she didn't want to be upstaged (I'm REALLY nothing special, by the way, that's just what bf reported to me. These things are all relative). Anyway, long story short, the friendship group was far more important to the bf than I was, and for this and many many many other reasons we split up after another year or so.
All a long-winded way of saying that maybe they see you as an imposter, someone who doesn't really fit in. In which case, you're better off without. If you stay with the bf he's going to have to choose between you and that's awkward too. This couple have really put a strain on your relationship, and it may not be accidental.