What is the Halachik source for women covering their lower legs (past the knee)? And why would sheer stockings be acceptable if the point is to cover the lower leg?
The Talmud (Brachot 24a) mentions the calf (ie. the body segment of the leg with two bones) as a place on a women's body which was normally covered. Many Rishonim1 explain that this is mentioned to teach that the status of a covered body part for women is independent of its also being a covered body part for men (which, apparently, the calf wasn't at the time), while other explain that it was mentioned to teach that the status of covered body part applies even if it is occasionally uncovered for some reason (which, apparently, women's calves were at the time). Accordingly, this specific example is not quoted by the Rambam or Shulchan Arukh.
If for whatever reason one thinks our dress patterns must conform to theirs, then this would be the primary source for their dress patterns regarding the calf.
1 eg. Eshkol, Raavad, Sefer Hashlama, Sefer HaMeorot, Sefer HaBattim, Raah, Rashba, Shittah Mekubbetzet. See Beit Yosef OC 75 who, quoting no other explanations, apparently takes the first position and seems to interpret the Tur accordingly.
Regarding opacity: the Halacha states (Brachot 25b, Shulchan Arukh OC 75:6) that seeing Ervah through glass is problematic, so covering with something relatively transparent would not seem to accomplish much, even if you argue that it is more modest than nothing.