The bottom "square near to base with 4 dots" looks like it could be BB with the first B reversed.
Looks like that to me too. BB, with one B reversed.
No sure if anything here -- but here is a good long list of *several glass marks*. Worth the look, and worth book-marking this page too ( I think)
http://www.myinsulators.com/glass-factories/bottlemarks.htmlLists a Berney Bond, Bellaire Bottle, Baker Bros.....

??
I do not think this list applies to *just Bottles*, as I saw
E.O Brody listed there, and we all know they
made Vintage Vases too. So maybe worth a look, or just worth keeping that list for a reference for stuff down the road.
?? Merely a suggestion :huh: