The evidence available suggests that much of the gold and silver coinage which came to India from Rome was (1) melted down to produce local coins and jewelry, (2) defaced by local rulers and used locally, and (3) hoarded for financial or religious reasons.
As noted by the OP's sources, huge amounts of gold and silver were shipped to India to buy luxuries which were then shipped back to Rome. Once in India,
these Roman coins had, at different times and regions,
multifarious uses—local currency, jewelry, ritualistic offerings at
Hindu and Buddhist shrines. Sometimes, the Roman gold coins were
melted to produce local coins and/or jewelry (Suresh, 2004), But a
large number of the Roman coins, in all metals, were used as
Hermann Kulke & Dietmar Rothermund, in A History of India (4th ed., 2004) note the contrast between southern India and the Kushan north:
The trade with Rome brought large numbers of Roman gold coins to
southern India. In contrast with the Kushanas who melted down all
Roman coins and reissued them in their own name, the rulers of south
India did not do this but simply defaced the coins. A sharp cut across
the face of the Roman emperor indicated that his sovereignty was not
recognised but his coins were welcome and would be accepted according
to their own intrinsic value.
"Roman gold coins excavated in Pudukottai, Tamil Nadu, India. One coin of Caligula (37–41 CE), and two coins of Nero (54–68). British Museum." Source
S. Suresh, in Symbols of Trade: Roman and Pseudo-Roman Objects found in India, notes that coin finds in southern India are far more numerous than elsewhere. This makes sense if Roman coins were melted down elsewhere. In Kushan, for example, Kanishka I (c. 127–150 AD), "melted Roman coins and modelled his on them."
On the hoarding of coins in southern India (during the Sangam period), there is some disagreement among academics as to why this was done. Suresh, in largely dismissing the idea that it was done because of local wars (he notes the time-frames don't fit), suggests that because
the early indigenous coins of south India were invariably thin small
pieces of silver or copper whereas the Roman issues in gold and silver
were heavier and artistically superior...the latter were often hoarded
in large numbers mainly for their bullion value.
Further north, during the Satavahana dynasty, silver punch-marked coins were issued by traders' guilds rather than by the state. However, we lack conclusive evidence that the silver was originally Roman. Roman coins were also melted down into bullion to make jewelry such as imitation Roman coin pendants.
Large hoards have been found buried, including under temples or shrines, in graves and at other sites (though it should be noted here that often only a small percentage of the coins are Roman). Some of this may have been intended for retrieval but much of it was ritualistic offerings.
Also, Raoul McLaughlin, in Rome and the Distant East: Trade Routes to the Ancient Lands of Arabia, India and China notes that India
channelled Roman wealth into the land of the ‘Seres’, or ‘Silk
Himanshu Prabha Ray, Trade in the Western Deccan under the Satavahanas (1985)
A. R. Mukhamedjanov, Economy and social system in central asia in the kushan age (UNESCO, 1996)
Unearthing Roman coins