Halāyudha actually quotes vareṇyam -> vareṇiyam as an example of the metrical reconstruction. Also kātyāyana also apparently gives some rules to justify such a process (like svaḥ to suvaḥ). But in practice only for sāmagāna this reconstruction is applied during pārāyaṇa.
vareNiyam
(ṇya -> ṇiya using the iyādi pūraṇah sūtra from chandaśśāstram)
Some use only for japa but not arghya & prāṇāyāma (AM), some use for japa & prāṇāyāma but not arghya (M3), some use for just arghya but not japa and prāṇāyāma (some TN śrautins), some prescribe it just for homa (some TN smārta manuals) while some don’t use anywhere (most TN smārtas)
The usual Telugu and Kannada brom quotation that I am aware of is “arghyakāle vareṇyaṃ syāt, japakāle vareṇiyam” (also pāṭhakāle in some versions)