By R’ Sternbuch’s chiluk, do you mean the one in chelek 4? I don’t understand why Matan Damim is more like tzitzis, as opposed to Lulav. The mitzva is to do the nesina, a din on a gavra.
As for Bal tigra, see Moadim Uzmanim 1, 25 in footnote and you will see R’ Sternbuch is Lshitaso, however it is clear from what he wrote there that he does not know of the Bais Halevi.
Rav Tavgar’s point is only in the Rambam and it won’t help for the Raavad. And also it is very debatable, because the Mishkenos Yaakov and others learn the rambam 1,4 that all techeiles is passul. If the mitzva is only the wrapping, how is it possible to make all techeiles? [But there are many strong reason not to learn the rambam like that]
And yes, I am curious to see your paper, and hope something can be arranged