Well let's talk about what's "out there", OK?
Colerain makes a .58 caliber 36" straight side, octagon barrel for $185 and the same thing in 42" for $200 from Track of the Wolf. Send it to Mr. Hoyt to have it converted to .62 and you're talking $260-$285 plus shipping both ways.
Colerain also makes their "Edward Marshall" rifle barrel in .58, swamped, octagon, and it might be thick enough to be converted to a smooth .62. It runs $215 from Track of The Wolf.
That's a lot higher in price than simply accepting an octagon to round smoothbore barrel, and it might be the only way to get a gun that fits a certain area and time period.
So that leaves either a pricey, custom option, OR you search for a 1" wide, .54 caliber used rifle, say something from TC in a Hawken, and see if Bob Hoyt can bore that out for you. Not super authentic, but short, probably light, and a .62 smooth rifle for not a whole lot of money.
LD