My Great-Grandmother and her sister are the only one's of the family line who survived the Armenian Genocide (as a 9 year old and as a 5 year old respectively) and my Great-Grandmother wrote about it extensively before she passed 15 years ago. Further, my Grandmother was born in Syria and emigrated to the U.S. before World War II. She has also written her story. Are they preservable as family memories or as something more?
Memoirs are one of the classic examples of primary historical sources!
Something like those documents are a look into historical events through the eyes of someone who experienced them directly, and they can be used - as carefully and as critically as any other source is used - to add to and evaluate how we understand those events.
Things like memoirs usually aren't (intentionally) formal scholarship, which is what I assume you're thinking of when you mention "unsupported claims." Assuming they aren't wildly off-base (e.g., claiming the genocide was at the hands of Martians), what primary source do is provide some of that support to scholarship. The historian's usually somewhat removed in time from the event they're studying, and documents like that can be a couple of bricks, made by someone much closer to the original events, that help firm up whatever structure the historian's trying to make.
Documents like those might not necessarily provide any grand worldshaking changes to what is known about the Armenian Genocide (though you never know). They almost always help to provide a little more detail. They'll fill in some tiny blanks, clarify a little about what might have happened in a particular village, maybe corroborate another story written by another survivor which mentions a particular event. A lot of the big narrative histories people read are built from things like that, relying on scores, hundreds, or thousands of little pieces building up over time.
At the more immediate level, you've also got in your hands what are probably a couple of very human individual stories about a terrible event, written by people whose survival is apparently the reason you exist in the first place. There's tremendous personal value there, alongside and independent of the professional or academic potentials. I can't speak to the latter obviously, since I don't actually have the stories on hand and I'm not exactly a specialist in the Armenian Genocide to begin with, but I am sure there are researchers and not a few museums or other institutions who would find stories like that interesting.
Questions of accuracy, detail, bias, and so on are going to be in there, of course, because those questions follow any historical source around. They even apply to the most staid, boring documents; a good historian will examine even things like census records, meeting minutes, or newspaper classifieds with a careful and occasionally jaundiced eye. Personal stories get some of that for obvious reasons, but they also often get some specific respect in the form of acknowledging the voice and agency of the person who wrote them. It might not be The Definitive History Of What Happened^TM, but it's still the account of someone who lived through an event, as expressed by that person directly.
(I recently finished a few years' work at an immigration museum where the bulk of the intangible collection was oral histories and written stories donated by people who'd passed through the facility, the bulk of them in the immediate postwar period. I might get just a little excited hearing about people finding things like that among their relatives' writings...)
This is absolutely something an archives would collect, and (I'm an archivist) I have processed non-published memoirs many times before, they're something we value. Don't worry about them being "unsupported" or written after the event - trained historians would still use your grandmother and great-grandmother's memoirs as a tool in telling history even if they'd mis-remembered some facts or timelines, and there are particular methods and techniques for using memoirs and oral history recordings and fitting them with other historical records. If you'd like help finding an archives to donate them to give me a PM (I'll want to know where you live and such) and I'll try to find you a good home for them. :)
Do you live somewhere near a university? If so, contact their history department and/or special collections library. These are absolutely valuable resources. In particular, look for someone who works with memory, oral history, or a subject related to (geographically) Armenia.
The library can tell you how to best preserve documents if your relatives wrote them down a long time ago, while the history department can help you determine how such accounts might be used by scholars. If they can't help you specifically, they should hopefully be able to point you in the right direction.