In answer to the question about origin...I don't know,either.
Quackenbush WAS a manufacturer of (as far as I know) lower grade .22 rifles ,the typical "boys rifle" of the time,approx turn of the century.
But I would not make the leap to say your rifle had anything to do with that company...unless a decendant of the Quackenbush family line crafted it.
As I look at it,it does not seem to show the patina of honest aging.
It does not look like its been around since 1850 or ?.
But there has long been a core of folks who enjoy burning black powder in muzzle loader rifles.
Some of them,like myself,decide to build their own rifle.
The movie "Jeremiah Johnson"ignited a surge in interest in muzzle loader rifles.
We had a great black powder rifle shop in town,"Cache la Poudre Rifleworks".
Unfortunately,the owner passed away...
He kept,among other things,stock blanks,custom barrels,locks and lock kits,and all the bits and pieces to build rifles.
There are also catalogues like "Track of the Wolf" which cater to muzzle loaders.
If I had to guess,and I COULD be wrong,I'd say a black powder enthusiast put some love into building his own personal custom rifle.
What happened next? Pure speculation,an estate sale.
Value? Subjective. Market would likely not be much,if my theory of origin is correct.
However,"gun buy back"means destruction.That rifle hardly represents any threat to anyone.I would never participate in such a program,even to game it.
Muzzle loaders are not typically heavily regulated.
I doubt it would be difficult to find some Father/Son or Daughter team that would greatly enjoy time together shooting that rifle.
I suggest,put a little effort into finding them.You might make a great Christmas for someone.
Which would make you feel better? Passing it to someone who will enjoy it,,or participating in an anti-gun political program?
The rifle LOOKS to me like it would be a good shooter,though it should be checked by a knowledgeable person or gunsmith.
I'd make someone happy.Just give it to them,before I would go "buy back"