Hi Sam,
Congratulations on your project. One has to be commanded to even attempt such a rescue.
It turns out that the overwhelming majority (read all) of US guns with barrels described as "Bernard" were not made by Leopold Bernard. One could order "Bernard" style barrels from the Belgian trade and that's where all those barrels came from. Your Sauer is similar, I am certain.
LB had a touchmark that he used from the 1840s until the end of the company in the early 1900s. Those barrels also had the serial number and date or date code on the lower rib.That is well documented in previous threads. If yours does not have it, by definition it is not a true Bernard.
LB was an ultra-premium barrel maker for most of his carrier including after his death in the 1870s. Barrel sets produced were very few for many decades of production. I think annual production was around 500 per year.
Many barrel makers copied the style of his touch mark including an E. Bernard from Belgium, who produced tons of fake L Bernards.
It does not really matter anyhow. Enjoy your Sauer for what it is!
Kindest regards,
WC-