Shotgun approach
Isn't that basically how the "shotgun" approach works to sequence DNA? They sequence bits and pieces, then "glue" them together.
But after 10 half-lives, there wouldn't be many long pieces left. I suppose if you had enough DNA, you might get lucky and find enough long pieces still intact.
BUT! If the half-life is only 521 years, then 10 half-lives is only 5210 years. A million years is like 2000 half-lives. So 65 million years is 100,000 half-lives. You would need to sort through an ENORMOUS amount of DNA before you'd find the necessary intact chains. I think that qualifies as a sisyphean task.