A little research about companies that made carriages in Rochester during this time revealed that the Cunningham Carriage Works was located on Canal Street.
Cunningham Carriage Factory & Showrooms 1882
The facility was huge and it appears to have been the only carriage building company on Canal St. The company was quiet famous and started in the 1840s and survived at the same location until the middle of the 20th century. The company made all types of horse drawn carriages including hearses and some very elegant and expensive carriages. They also won prizes for their carriages at the Philadelphia Exposition in 1876.
James Glover most likely was employed at this facility from 1873 - 1876 as a carriage trimmer. The trimming department was located on the 4th floor and was involved in the interior upholstery with fabrics and leather, adding mirrors, lamps, door handles and bells to carriages. Skilled workers earned $1 - $2 a day and unskilled were paid about half that amount. A statement in the history of the Cunningham Carriage Factory stated the skilled workers who were careful with their money often were able to save enough to buy a small house after only 1 year of work.
I haven't located any information about carriage companies on Exchange Street in Rochester, but I'm still looking.
For more reading about the Cunningham Carriage Works and some photos of their products see Coachbuilt