Well, there are many different translations of the story. From what I I remember, the original text is pretty much there. The "filling in" is pretty much guessing as to what specific (obscure) words mean -- not actually writing the story.
As far as textual evidence goes, I'm not sure that there are "stories" older than this -- but that brings up all sorts of issues as to what is a "story." You certainly have some recurring themes that come out of Gilgamesh and other works like it -- a worldwide, disasterous flood, for instance(e.g. Noah's flood). And, if these did come from a single historical event, certainly the information got passed on (as I recall you see this even in South American cultures, but don't quote me). But whether or not it got passed on in writing or not is an entirely different question.
And, as far as those who were wondering, no I don't have a good date for the suggested writing date of Genesis, and my reference stuff is all at work. If you're interested (and I imagine few are) you'll have to figure it out on your own.
Have fun with Enkido and Gilgamesh.
