Wow, I hadn't realized that I even felt that way until I read your post. I had never really articulated this thought before.
I'm not Armenian, but my people (HK) group also stand at around 7m and dwindling, with our probably dying language, and a politically powerful persecutor who pretends to be our Lord and Savior. Our people haven't been around for near as long as you guys, but a number of what you said really hit hard: (1) the political situation breaks my heart, (2) I hadn't seen non-immediate circle folks of my people for a while ..., (3) that hole in my heart I don't usually realise is there.
It reminds me of watching the new Trek movie, when Spock realises he is now a member of an endangered species.
Do you think.... if certain things of your culture will persist long after the last one of you perish, what might they be?