Does your carbine have a Stabler cutoff?
I'm not sure what you mean by Burnside "rifle production." Burnside made Spencer and Burnside carbines and, I believe, early in the war a very very few Burnside patent rifles (using the "ice cream cone" percussion cartridge), but I am not aware of Burnside-manufactured Spencer rifles other than the ones converted from carbines by Springfield Armory in the 1870s.
Do you have photos? They could be helpful and educational.
--DJ