If we are looking for all possible combinations that could derive tēvanti in Tamil purely based on possible sound transformations, then here are the possibilities.

1. Word-initial t- in Tamil could be derived from:  t-, d-, dh-, sth-, sn- and c.

2. Word medial -v- in Tamil could be derived from: p, b, m, v

3. Final suffix -nti could be arrived at from: -nti, -ndi, -ntya, -ndya

If I feed these possibilities to my program it generates the following combinations:

tēmanti, dēmanti, dhēmanti, sēmanti, ṣēmanti, śēmanti, snēmanti, sthēmanti, cēmanti, tāmanti, dāmanti, dhāmanti, sāmanti, ṣāmanti, śāmanti, snāmanti, sthāmanti, cāmanti, tēmandi, dēmandi, dhēmandi, sēmandi, ṣēmandi, śēmandi, snēmandi, sthēmandi, cēmandi, tāmandi, dāmandi, dhāmandi, sāmandi, ṣāmandi, śāmandi, snāmandi, sthāmandi, cāmandi, tēmantya, dēmantya, dhēmantya, sēmantya, ṣēmantya, śēmantya, snēmantya, sthēmantya, cēmantya, tāmantya, dāmantya, dhāmantya, sāmantya, ṣāmantya, śāmantya, snāmantya, sthāmantya, cāmantya, tēmandya, dēmandya, dhēmandya, sēmandya, ṣēmandya, śēmandya, snēmandya, sthēmandya, cēmandya, tāmandya, dāmandya, dhāmandya, sāmandya, ṣāmandya, śāmandya, snāmandya, sthāmandya, cāmandya, tēvanti, dēvanti, dhēvanti, sēvanti, ṣēvanti, śēvanti, snēvanti, sthēvanti, cēvanti, tāvanti, dāvanti, dhāvanti, sāvanti, ṣāvanti, śāvanti, snāvanti, sthāvanti, cāvanti, tēvandi, dēvandi, dhēvandi, sēvandi, ṣēvandi, śēvandi, snēvandi, sthēvandi, cēvandi, tāvandi, dāvandi, dhāvandi, sāvandi, ṣāvandi, śāvandi, snāvandi, sthāvandi, cāvandi, tēvantya, dēvantya, dhēvantya, sēvantya, ṣēvantya, śēvantya, snēvantya, sthēvantya, cēvantya, tāvantya, dāvantya, dhāvantya, sāvantya, ṣāvantya, śāvantya, snāvantya, sthāvantya, cāvantya, tēvandya, dēvandya, dhēvandya, sēvandya, ṣēvandya, śēvandya, snēvandya, sthēvandya, cēvandya, tāvandya, dāvandya, dhāvandya, sāvandya, ṣāvandya, śāvandya, snāvandya, sthāvandya, cāvandya, tēpanti, dēpanti, dhēpanti, sēpanti, ṣēpanti, śēpanti, snēpanti, sthēpanti, cēpanti, tāpanti, dāpanti, dhāpanti, sāpanti, ṣāpanti, śāpanti, snāpanti, sthāpanti, cāpanti, tēpandi, dēpandi, dhēpandi, sēpandi, ṣēpandi, śēpandi, snēpandi, sthēpandi, cēpandi, tāpandi, dāpandi, dhāpandi, sāpandi, ṣāpandi, śāpandi, snāpandi, sthāpandi, cāpandi, tēpantya, dēpantya, dhēpantya, sēpantya, ṣēpantya, śēpantya, snēpantya, sthēpantya, cēpantya, tāpantya, dāpantya, dhāpantya, sāpantya, ṣāpantya, śāpantya, snāpantya, sthāpantya, cāpantya, tēpandya, dēpandya, dhēpandya, sēpandya, ṣēpandya, śēpandya, snēpandya, sthēpandya, cēpandya, tāpandya, dāpandya, dhāpandya, sāpandya, ṣāpandya, śāpandya, snāpandya, sthāpandya, cāpandya, tēbanti, dēbanti, dhēbanti, sēbanti, ṣēbanti, śēbanti, snēbanti, sthēbanti, cēbanti, tābanti, dābanti, dhābanti, sābanti, ṣābanti, śābanti, snābanti, sthābanti, cābanti, tēbandi, dēbandi, dhēbandi, sēbandi, ṣēbandi, śēbandi, snēbandi, sthēbandi, cēbandi, tābandi, dābandi, dhābandi, sābandi, ṣābandi, śābandi, snābandi, sthābandi, cābandi, tēbantya, dēbantya, dhēbantya, sēbantya, ṣēbantya, śēbantya, snēbantya, sthēbantya, cēbantya, tābantya, dābantya, dhābantya, sābantya, ṣābantya, śābantya, snābantya, sthābantya, cābantya, tēbandya, dēbandya, dhēbandya, sēbandya, ṣēbandya, śēbandya, snēbandya, sthēbandya, cēbandya, tābandya, dābandya, dhābandya, sābandya, ṣābandya, śābandya, snābandya, sthābandya, cābandya.

For your laughs only!

Regards,

Suresh.

PS: I still think c/sV̄mantī 'Indian rose' is the most plausible candidate, as it reasonably explains the variant spellings of tēvanti and tāvanti.

PPS: I totally agree with you that "a barren woman of the gods" doesn't make much sense at all.