Although I disagree with your presupposition that the ages are merely symbolic, I think this is a great question nonetheless. The reason I say this is that regardless of whether the ages are historically significant, we should assume they are literarily significant. The Bible is literature, and each author (or redactor) of each book has crafted his work of literature with a particular purpose in mind. What the author does include should be considered significant, since it was selected for inclusion while so many other details were left out. (This is often referred to as the "principle of selectivity".) The author could have just skipped the ages altogether if they were merely historical data points; there are plenty of other details the author leaves out, after all.
Short Answer: With that said, I believe the textual evidence points toward the ages being very significant in advancing the author's theological agenda. These ages show how the world changed after the flood, and how human life made the enormous transition from the original, exalted state of creation to the "modern", decrepit state of things (at the time of authorship.)
Here is a chart of the ages of the Patriarchs prior to the Israelites' time in Egypt, normalized by birth date:
The green are the ages of people who were born and died prior to the flood1
The yellow are the ages of people who were born before the flood, and died after the flood
The red are the ages of people who were born and died after the flood
What the author shows us is that prior to the flood people lived a really, really, really long time, but then the flood changed things. Since I mapped the ages by birth date and not merely by textual entry the "taper" isn't as clear in the previous graph, so here is another graph of the post-flood ages that shows the post-flood taper more clearly:
You can see that while it is not a perfectly smooth curve, the trend does show, over all, the degradation of the human lifespan following the flood.
The flood is a major catastrophic event in Genesis, executed because of man's great wickedness. The author wants the audience to see that things used to be much better than they are "now," but because of man's great wickedness, God executed judgment on the human race, and it had an enormous negative effect on our lives. The trend is intended to show the readers that their lives would have been much better if man hadn't sinned so greatly against God.
As for the ages being very specific and the curve not being perfectly smooth, I would suggest that the author intended for the reader to take these ages to be real ages. (Whether or not they are is another topic.) If the author had simply chosen symbolic ages along the lines of "900 . . . 900 . . . 900 . . . 900 . . . 700 . . . 500 . . . 300 . . . " it would not have been as believable, and would not have had the same effect on the reader as it would to relate these men to their own real, physical heritage. In other words, the "realness" of the ages brings the story home for the audience.
1: I left out Enoch, since the text explicitly claims that he was caught up to heaven before he could live out his days and die.