Looking at your dimensions and the caliber Old Dog I think a rifle with that small of a bore and that dimension of barrel would be heavy for caliber . The old timers were stuck with soft forged iron and whatever skill and luck ,they, or someone could muster that week forging a barrel , maybe thinking if the 1st borehole showed occlusions and pits they could keep reaming it till they found a nice clean bore to rifle .
Now if you really want that barrel it can be made or you could even hand swamp it draw filing it l . Some of the skilled machinists can chime in but machine swamping the barrel might put stresses on the barrel .
Personally I would pick a close- is- good 44'' stress- relived barrel and look at the barrel weights before ordering .If what you were looking at is still too heavy (c' weight at .45 ?) I would consider going up to 50 cal .The particular details, the stocking, the wood , the inlays and the furniture is what I would be focusing on with the idea of making something very very close , in his style, maybe made a few months before or after .
I've never really been fully happy with anything i've built but the guns I liked better were the ones that handled the best .Some originals were very fetching but absolute tanks to handle and nose heavy which were joy killers .
There is an apocryphal story about the introduction of the gun to Japan ...It seems that one of the crew of the 1st European ships threw a gun overboard one day .This was seen by the Japanese on shore who immediately sent a guy to retrieve it as they wanted this technology very much and upon securing it took it to their best metal smiths to duplicate it . Turns out it didn't work . The European who threw it overboard did so in disgust at it wasn't working and that the Japanese had copied it so closely they duplicated the defect.
No one would throw a gun overboard of course and no smart Japanese metalsmith would make a flawed weapon but the story does remind me that not everything built back in the old days was so great .( and of course it plays to the ''copy it'' prejudice some times deserved sometimes not )
If I were building the gun for a client I would have them source out the said barrel as it might be years in the making , cost way more than a regular well made swamped barrel , or end up being overweight ,none of which is in their interest but I'd let them figure that out on their time and money not mine . It's your project of course.