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Would it be enough time? Sure. Let's say man appears 40K ago. Mutation rates from 40-11K ago are about the same as today. From 11-7K ago they average 10 times the current rate due to the Vela Supernova(see below). So for more than 1/10th of our existence cosic radiation was ten times its current rate. If this caused mutations in a linear fashion, as the mouse study you linked to suggested, then this implies that the "apparent DNA" age of man is about twice his actual age. Not 80K, but 40K, same time as the artifacts show up.

I found this from the reasons.org site...
paper entitled "Terrestrial Paleoenvironmental Effects of a Late Quaternary-Age Supernova" was published by geophysicist G. Robert Brakenridge in the journal Icarus (v. 46, pp. 81-93). Dr. Brakenridge describes measurements that date the Vela supernova as having occurred sometime between 9300 and 6400 B. C. (A supernova is the cataclysmic explosion of a massive star; this one is called the irela supernova because it occurred in the Vela constellation.) These dates fit well with the Biblical date for the Genesis Flood.

Dr. Brakenridge also points out that this supernova occurred about three times closer to Earth than any other supernova event in human history. Thus, it is probably responsible for most of the cosmic rays that now come our way, cosmic rays which break down protein. Further, the Vela supernova would have affected the upper atmosphere in such a way as to bring about a global cooling and would have damaged the ozone layer so t:, as to increase ultraviolet by two to ten times. Dr. Brakenridge documents geological evidence for both effects in the era between 8,000 and 9,000 B. C., also the time of the disappearance of some diatom and plankton species.