It's not accurate that the suttas do not address aversion (dosa) and the antidote for it.
For example, in the Nakulapita Sutta, the Buddha advises householder Nakulapita with regards to his aversion to old age and disease:
Then the householder Nakulapita went to the Blessed One and on
arrival, having bowed down to him, sat to one side. As he was sitting
there he said to the Blessed One, "Lord, I am a feeble old man, aged,
advanced in years, having come to the last stage of life. I am
afflicted in body & ailing with every moment. And it is only rarely
that I get to see the Blessed One & the monks who nourish the heart.
May the Blessed One teach me, may the Blessed One instruct me, for my
long-term benefit & happiness."
"So it is, householder. So it is. The body is afflicted, weak, &
encumbered. For who, looking after this body, would claim even a
moment of true health, except through sheer foolishness? So you should
train yourself: 'Even though I may be afflicted in body, my mind will
be unafflicted.' That is how you should train yourself."
Later, Ven. Sariputta explained this in more detail to Nakulapita, which incidentally provides the antidote for aversion (dosa) through the contemplation of not-self (anatta):
"And how is one afflicted in body but unafflicted in mind? There is
the case where a well-instructed disciple of the noble ones — who has
regard for noble ones, is well-versed & disciplined in their Dhamma;
who has regard for men of integrity, is well-versed & disciplined in
their Dhamma — does not assume form to be the self, or the self as
possessing form, or form as in the self, or the self as in form. He is
not seized with the idea that 'I am form' or 'Form is mine.' As he is
not seized with these ideas, his form changes & alters, but he does
not fall into sorrow, lamentation, pain, distress, or despair over its
change & alteration.
"He does not assume feeling to be the self...
"He does not assume perception to be the self...
"He does not assume fabrications to be the self...
"He does not assume consciousness to be the self, or the self as
possessing consciousness, or consciousness as in the self, or the self
as in consciousness. He is not seized with the idea that 'I am
consciousness' or 'Consciousness is mine.' As he is not seized with
these ideas, his consciousness changes & alters, but he does not fall
into sorrow, lamentation, pain, distress, or despair over its change &
alteration.
"This, householder, is how one is afflicted in body but unafflicted in
mind."
When the Buddha visited the sick ward of monks in Gelañña Sutta, he advised the contemplation of impermanence (anicca), which also works as an antidote for aversion (dosa):
"Sensing a feeling of pleasure, he discerns that it is inconstant, not
grasped at, not relished. Sensing a feeling of pain... Sensing a
feeling of neither-pleasure-nor-pain, he discerns that it is
inconstant, not grasped at, not relished. Sensing a feeling of
pleasure, he senses it disjoined from it. Sensing a feeling of pain...
Sensing a feeling of neither-pleasure-nor-pain, he senses it disjoined
from it. When sensing a feeling limited to the body, he discerns that
'I am sensing a feeling limited to the body.' When sensing a feeling
limited to life, he discerns that 'I am sensing a feeling limited to
life.' He discerns that 'With the break-up of the body, after the
termination of life, all that is sensed, not being relished, will grow
cold right here.'
"Just as an oil lamp burns in dependence on oil & wick; and from the
termination of the oil & wick — and from not being provided any other
sustenance — it goes out unnourished; in the same way, when sensing a
feeling limited to the body, he discerns that 'I am sensing a feeling
limited to the body.' When sensing a feeling limited to life, he
discerns that 'I am sensing a feeling limited to life.' He discerns
that 'With the break-up of the body, after the termination of life,
all that is sensed, not being relished, will grow cold right here.'"
OP: [comment] I was hoping that this topic would be more about choosing or failing to do what one is or feels averse to -- to some
extent Nakulapita's growing old wasn't a choice (extent to the extent
of choosing to identify with form, feeling, etc.).
In Vajjiputta Sutta (quoted below), the monk alone in the forest, heard music and festivities in a neighbouring village, and felt aversion towards his seclusion (which is considered good for monks by the Dhamma). This is an aversion by choice (unlike disease and old age), which was overcome by changing his perspective or changing his view of the situation.
On one occasion a certain monk, a Vajjian princeling, was dwelling
near Vesali in a forest thicket. And on that occasion an all-night
festival was being held in Vesali. The monk — lamenting as he heard
the resounding din of wind music, string music, & gongs coming from
Vesali, on that occasion recited this verse:
I live in the wilderness all alone
like a log cast away in the forest.
On a night like this,
who could there be
more miserable than me?
Then the devata inhabiting the forest thicket, feeling sympathy for
the monk, desiring his benefit, desiring to bring him to his senses,
approached him and addressed him with this verse:
As you live in the wilderness all alone
like a log cast away in the forest,
many are those who envy you,
as hell-beings do,
those headed for heaven.
The monk, chastened by the devata, came to his senses.
I agree with Andrei: In this answer, by understanding the underlying reasons for others' sufferings, we can generate compassion towards them. This was proposed as an antidote towards contempt. This is one example of overcoming aversion by changing one's perspective or view of a situation.
In fact, disgust (nibbida) to cure passion (lobha), compassion to cure contempt, not-self or impermanence to cure aversion towards old age or suffering, and changing one's perspective to cure aversion towards skillful things like seclusion, are all examples of changing one's perspective or view of a situation, to turn unwholesome into wholesome.