Your last point needs to be emphasized more. The core mechanism of aging is likely to be very similar across species as aging affect all tissues, organs, etc.
The lifespan of humans is less than twice that of our closest relatives, and probably there is no coincidence in the fact that about the same ratio exists between the maturity age of humans and that of apes.
Aging in humans does not seem to have any qualitative difference, it just happens slower, like also the maturity.
Besides, the apes in general age in an unusual way. All take too long to mature compared to their lifespan, and all have too long a lifespan compared to their size (the mammals have a rough correlation between lifespan and size). Yes, we are merely at the extreme of that weirdness, not in a new category of weirdness. But it still means we are different from mice in some way.