Putting this all together, I therefore read Estrei Alφazei as 'before Ashtarte with Calf' in reference to a general religious theme that existed across several Mediterranean cultures whereby a goddess of fertility like Ashtarte or Asherah is portrayed in the form of a mother cow with a bull as consort (representing an equivalent of Canaanite Baal) and she rears a son who's predictably in the form of a calf. One is reminded perhaps of later Egyptian worship revolving around a mother Isis holding the child Horus, or later still a mother Mary cradling the child Jesus in her arms.
Based on what I understand from my current reading of the Liber Linteus, this sacred bovine goddess was honoured in Etruria with a procession of people in which a lectica was carried piously with religious icons (cletram śrenχve = 'lectica with icons') and holy offerings consisting of cakes and slain pig.
It's interesting that the Etruscans were worshiping not only Greek and Roman deities but even Phoenician ones, however it's also to be expected given much documented Carthaginian influence on Etruria of which the Pyrgi Tablets are but a small part of the fuller picture. Etruscan culture was very cosmopolitan and relatively unxenophobic throughout the centuries since its inception due to the wide-spanning trade network reaching across the Tyrrhenian, Mediterranean and Adriatic seas. At one time, Etruria was the mirror to the ancient world which readily supplied all of its lavish riches. So it wasn't difficult for the average Etruscan to look outwards to other cultures for inspiration and to refer even to native gods with the closest equivalents in foreign pantheons. No doubt one's prestige in Etruria was built in part from this characteristic quest for the exotic.