Hi Richard, I too am a descendant of the Bourques from Sackville,New Brunswick. My bourques came from New Brunswick in the early 1900's to Lynn,Mass also. They lived and are buried in Lynn. They also changed the spelling from Bourque to Burke. You may want to try and check out this web site. www.gnb.ca They have a lot of info on this site that may be usefull. If not, try posting something on the New Brunswick List . Maybe some kind sole will be able to find them in the census.
I have a few copies of the Lynn city directories. I did find a Eugene Bourque in the 1915 directories. Eugene Bourque was a Boarder at 101 Newhall. He was a carpenter. He also shows up in the 1930 directories as a carpenter living at 571 western Ave. If you can get the names of Eugenes parents, you may be able to better trace them to Antoine Bourg. Good luck and if you need help, let me know, I will be glad to help. Cathy