The question seems to misconstrue the idea of "momentariness".
"Momentariness" does not mean everything exists for a "moment". "Momentariness" is merely the recognition that consciousness & thought arises for a moment (but other things do not necessarily exist for a moment).
SN 12.61 may help, here:
It would be better for the uninstructed run-of-the-mill person to hold to the body composed of the four great elements, rather than the
mind, as the self. Why is that? Because this body composed of the four
great elements is seen standing for a year, two years, three, four,
five, ten, twenty, thirty, forty, fifty, a hundred years or more. But
what's called 'mind,' 'intellect,' or 'consciousness' by day and by
night arises as one thing and ceases as another. Just as a monkey,
swinging through a forest wilderness, grabs a branch. Letting go of
it, it grabs another branch. Letting go of that, it grabs another one.
Letting go of that, it grabs another one. In the same way, what's
called 'mind,' 'intellect,' or 'consciousness' by day and by night
arises as one thing and ceases as another.
That SN 12.61 says the physical body can be seem to last for a long time supports the view in the question that tendencies & memories are stored in the brain. Personally, I don't see the point of speculating about scriptures in the situation where both science & personal experience tell us where latent tendencies & memories are stored. You know as an observable fact that brain injury impairs memory therefore what is the point of denying this reality and seeking to explain it in an alternate speculative unknowable way?
In MN 64, the Buddha said the underlying tendencies exist within the new born child, even though these underlying tendencies are yet to arise into the child's conscious mind. The Buddha said nothing about "past lives" here. The underlying tendencies are natural elements (dhatu). They have no relationship to past lives. Men & women are born with sexual organs and sexual apparatus (such as a womb). When their bodies mature, these sexual tendencies start to produce chemicals and hormones which result in the salient arising of sexual lust in the young man and young woman. We can see through mere observation that the growth in the mental defilement of lust is related to the growth & maturity of the physical body.