Well, we aren't purely stochastic machines passively subject to entropy. We also have some DNA repair mechanisms, which work better when we are younger, and maybe could be restored to their youthful function. Plus, if a cell is beyond repair, other mechanisms can simply whack it and it will later be replaced by a new cell grown from the stem cell population (of course with some limits). But that again means having a youthful stem cell population.

This is an uninformed suggestion, but is it possible to take a large collection of cells from across the body and work out which ones carry the untainted DNA by statistical methods?