I think you are on the right lines. Those two items were never together on a proofed and accepted rifle. I recommend a book for all the details: "Remington Rolling Block Military Rifles of the World" by George Layman, Andrew Mowbray Publishers, ISBN 1-931464-45-6 is way out in front of whatever's coming second.
I think you should measure the bore a.s.a.p. to reduce the the possibilities.
It would have been helpful if you had said what the barrel length is, instead of "several inches longer", as I do not know with which model you are making the comparison. The Spingfield-Remington Model 1871 had a 36" barrel, Are you sure your barrel is several inches longer than that?
Please check these two dimensions and report back, then we can narrow the choice down a bit.
Patrick
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