Dear Louise, I was going through the Forum messages and yours caught my eye.
I do not know how much help this will be but your question about T.O. Brith Abraham was familiar to me. But I believe the "T" is suppose to be an "I". It stands for the "Independent Order of Brith Abraham". It is just one of many Jewish fraternal organizations that thrived in and around New York especially during the last part of the 1800's and early part of the 1900's.
I tried looking them up and contacting them but it has been a long time and I do not remember much but that it was a dead end. I found that they existed but that was about it.
My guess is that some of those fraternal organizations may have merged with others as the membership became increasingly old and less involved, or died out. The membership books will still be around somewhere
Those records are with someone or some existing organization somewhere. My G-Grandfather Jacob Friedman was probably a member at the same time as he was living in NY in 1887 when he married my G-Grandmother Jennie (Newirth) Friedman.
I live in Israel now, so it is hard for me to get much that is not on the WEB.