interesting Drew.
Distant relatives, the Losey barrel mill was in Brocktondale, in the town of Caroline NY - (Losey-Lull for a time) the sons having moved from their father's Trumansburg NY "gun factory".
According to a note I saved from a Walter Snyder post here done back in 2007 - Bob Edwards lived across the road from the barrel mill. From the history I have seen - the barrel mill did not produce shotgun barrels. But Mr Snyder's comment said Bob Edwards was connected to Ithaca in 1883, at which point I believe the Losey millhad gone out out busines and the building converted to a blanket factory.
also - just a thought - the image above lists Bob Edwards as a "barrel borer" not a maker. doesn't a barrel borer finish tubes already made?