I normally stay out of this kind of topic because I just don't understand it, but my usual answer to the apparent great age of the universe is that time appears to be something different on the scale of astronomy than it is to us on Earth. I don't understand this, how it could be or what it means in terms of physics etc., but I keep thinking about the claims that a person traveling astronomical distances would not age as he would on Earth. That suggests that there is a big difference in how time works on these different scales, which seems to be related to what you are saying.
Edited by Faith, : No reason given.