Charles,
I question the conclusions of your provider. Just because a weapon falls into a range of known serial numbers issued to a particular regiment/company is meaningless information.
During the war of the rebellion up through the Indian Wars until 1877, weapons were not issued in batches of serial numbers or rarely recorded. (The one exception of those issued in a semblance of sequence was the Colt S.A.A. issued to the army in 1874 & they did replace all other revolvers & even those have some mixed numbers). Even at that it is only a guess what regiments were issued what serial numbers unless it was recorded for some reason like theft, repair, etc.
Sometimes a regiment or company may have needed only 10 guns out of a crate & maybe the numbers might be in sequence but a lot of times they weren't. What I saying, that the majority of weapons issued most likely weren't in order. Within regiments & sometime within companies it was not uncommon to have a mixture of Sharps & Spencer's or Colts or Remington's or any other make.
What your provider was doing was going to a likely list of known issued serial numbers provided by SRS.
Lets say he has a list of 1851 Navy Colts with serial numbers from 20001 thru 20005, issued to the 6th Iowa Cavalry. Now let's say your weapon is 20006 with no known history. Your gun is within the range but no real proof of being issued to the 6th Iowa Cavalry.
See what I mean?
This is a case of close but no cigar.
The only real way to prove a particular weapon was issued is to have actual proof by documentation.
There are very, very few weapons out of many that have such proof.
I hate to be a wet blanket but that is the way it is in collecting weapons with a pedigree.
Enjoy your 51 Navy knowing that it most likely saw the elephant but it's history will always be a mystery.