But in Dharmasutras, we do not find any provision for changing caste.
No.
There is a provision to change caste according to many scriptures. But, it needs extreme dedication, which is uncommon.
As you mentioned, there are several people in the scriptures who changed their caste.
Manusmriti also says about the possibility of changing caste but needs extreme austerities.
By the force of austerities and the seed they attain higher or lower
rank among men, through birth, cycle after cycle.
[42, 3:Status of the Mixed Castes, 10: Abnormal Social Conditions, Manusmriti]
Although it does not explicitly says that it happens at a single birth, we can notice from Sukra Niti that if the force of austerities, in following special penances, is significant enough then it is possible to change caste in a single lifetime.
Inferiority and superiority depend sometimes on the qualities of the
seed, sometimes on the character of the field. But excellence is due
to both. Viswamitra Vasistha, Matanga and Narada and others became
elevated by special penances not by birth.
[78-81, 4: Social Customs and Institutions, Sukra Niti]
Thus, dharma sastras have provisions to change the caste in a single birth. But it is extremely difficult to implement.