Interesting photos, twotimestalia. If there is more than 1 of these strange badges out there, I wonder if a chapter designed this for their own members pre-standard-badge era . They are all a little different in the placement of the large jewel and the engraving.
There are always badges on Ebay for many different sororities and fraternities at any given time, I wish we could get our hands on all of them but it just isn't possible.