Ross G Caldwell
Certainly I think you're right that 'punique' here means Phoenician, it is used in that sense for example here:
Introduction à l'Ecriture sainte... enrichie de plusieurs figures [par M. Ogier], trad. du latin du R. Père Lamy... par le P. François Boyer, 1699
The Phoenician/Punic worm was used to make a worm-dye (a dye from some sort of insect), and the word was used synonymously for the colour (a scarlet dye, used much by the Jews.) We have the word vermillion for example - the worm (ver) colour.
In the bible it is tola'ath shani - the scarlet worm. Production of the dye was perfected by the Phoenicians (according to Pliny), hence 'the Punic worm/Vermilion'. The arabic word is kermez which means both the worm and the colour.
So I think you are probably right with your reference to the Phoenician 'purples'.
I'm still very puzzled about how the letter relates to it, though. It remains, for me, a tentative possibility, but not a great theory.
But is there anything better? Augustine apparently listed some Punic words, I haven't looked into it yet. But it would surprise me if a Rabbi would rely on Augustine as an authority for anything as important as the meaning of a Hebrew letter. I'm sure there is a biblical solution, or, that the Rabbi was himself well acquainted with sister-tongues of Hebrew to make an etymological speculation.