If you and or you're sources have dated the Sumerian references by way of the "King's Lists'" (e.g., The Egyptian Kings' list versus/compared to the Sumerian Kings' list.) then that may explain the error in your personal studies/research. You see, when making the lists noting the genealogies, and more importantly the duration of reigns for individual kings, a lot of times the reigns overlapped one another, and yet they were listed as occurring sequentially.
A simple way to explain this is to use an example from the history of America. We both of course know that we've been around as a nation since 1776, which means America has been a nation for ~238 years; however, let's say the only records we had were today were records of the governors' terms of office from Georgia and from Virginia since we were founded in 1776.
If we listed those terms of office from both Georgia and Virginia sequentially, instead of how they actually occurred, which was concurrently, we could extrapolate an age of over 450 years for the nation of America. We'd be wrong, but if all we had were the durations of each respective governors' term of office, "we would believe we were right in our wrongness."
IMHO, if the ~3000 year age your referring to comes from extrapolations based on using the Kings' Lists, then they are in error due to how the record keeping was done back then. As far as the Holy Bible's record is concerned, the languages were divided sometime between the Flood account and the details concerning Abram (whom became Abraham) being recorded in the book of Genesis. Since the Flood occurred ~4,450 years ago, based on extrapolating the years from the genealogies listed, according to the Holy Bible the Hebrew language has existed since the Creation event, or ~6,000 years ago.
-PW