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I have and shoot an H&A underhammer. the long barrel 45 caliber round ball model they made. At one time I also had the 58 cal model. (foolishly swapped it off)

In the overall scheme of things, they may be slightly more accurate than the standard side lock percussion gun with a single trigger. First of all the dropping hammer is out of sight, so there is no cause for flinching. Second the fire is directed from the nipple immediately into the main charge instead of having to traverse a narrow flash channel or making a 90 degree turn through a drum and nipple.

The old H&A barrels were rifled with wider grooves and narrower lands which was slightly better for patched round ball accuracy. What the Green Mtn barrel may have I don't know.

As for the 1,00 yard shots. a 15 inch group at a 1,000 yds would win nearly any target match. He certainly didn't do it with a barrel made for patched round balls. It took a specialized barrel that probably had a false muzzle and a mechanical lever system for starting a cross patched bullet that weighed around 500 to 600 grains.

There is a club near Shartlesville PA where specialized bench rest guns compete. They are often underhammer guns with 2 inch thick or heavier barrels and those barrels are often 40 inches or longer. Sometimes the guns are six feet long and weigh 70 lbs. I went there to watcch a match once. They put flags out every 70 to 100 yds to watch for wind. I saw a 3 hole cloverleaf shot at 300 yds with a 62 caliber. Keep in mind that the gun you are considering is probably a good gun, but it won't repeat those feats.

I have PEEP sights on my H&A and it is about 65 inches long. I have shot 5 shot groups less than MOA at 100 yards from a bench. usually the 5 shot groups are about 1.75 inches. I can do ever so slightly better with a side lock perc gun with double set triggers and a target barrel.

You should read an account of the famous Creedmore Match of the early 1870's. The Irish National Team was tops in the world with extremely specialized muzzleloader guns, and accuracy wasn't anywhere near 15 inches at 1000 yds. That rifle match was so built up with hype, that thousands of spectators showed up to watch. What are the chances of that happening today?

 

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There's one or two suppliers that sell underhammer actions and you put your own barrels on them. At that point you need to determine what purpose the gun will have. Round balls guns are really only good to a max of 200 yds. after that the wind and trajectory makes fine accuracy a major problem. For long distances, you need a bullet and faster twist. There are dozens of styles of rifling. Some makers offer only one or two styles and those are general purpose. If you are after minute of angle accuracy, with either round ball or bullet, you will almost certainly need a custom barrel.

Years ago I talked to a guy named "Hoppy" who was a barrel maker. He suggested I read on on rifling styles and then call him again. Hoppy made a very special barrel for me for shooting round balls. Slow twist, grooves five times wider than the lands and the grooves were cut with round sides instead of square sides. I won alot of matches with that barrel. He even put a choked muzzle on that rifle barrel. Talk about some precision shooting. If you are going with a bullet barrel for long range, read up about Harry Pope's system of rifling and the muzzleloader centerfire guns he made. If I were going to build a long range barrel gun, I would use Harry's system and a false muzzle. For thousand yard shooting, anything less thhan a 45 caliber 500 grain bullet isn't sufficiently stable. A 40 caliber might be good to about 700 yds. There's another system of rifling that I don't believe anyone copies today, and that is Alexander Henry's sytem of rifling. the lands were round humps and even the grrooves had raised middles. His barrels were choked just in front of the chamber and again just at the muzzle. Having such a barrel made today would be extraordinarily expensive. With pure lead bullets, they were about the most accurate black powder military guns ever mass produced. Shooting hard lead bullets in aLEX HENRY barrels is dangerous.