Some more updated info on the shell lacy plates/bowls. From the hardbound catalog of the William J. Elsholz collection dispersed through Bournes Auctions in 1988 three examples are pictured. Two appear to be 6 in. plates and one cup pate. All have small differences in some way, either the center medallion differs, the star in the two diamonded base medallions may be omitted and the scalloped rim may or may not be stippled. They do not give a possible origin, except to say about the cup plate " origin uncertain".
Of the three versions pictured in Kenneth M. Wilson's book AMERICAN GLASS 1760-1930 Toledo Museum of Art 1994 all are different in some small way. The 6 in. bowl is missing the center medallion altogether. This is the version most often seen conjoined to a pressed base to form a compote. None of these examples, 6 in. bowl, cup plate and 6 in. plate have the star in two of the base medallions. Statements to origin only go as far as to say "probably Sandwich" for the bowl, 'probably New England" for the cup plate and "possibly Sandwich" for the plate.
A closeup of the center medallion would be most helpful. Your window picture [first one] very nice but too small to accurately make out the very center motif. Seems to be a handful of differing center motifs with these lacy shell plate/bowls.