Gumboman;
I fear your barrel is too short to utilize the required powder charge needed to stabilize the ball. Most of these big charges, you are firing is going out on the ground.
Hungry Horse
This old wives tale is never going to die it seems.
The question would be: "Is the velocity increasing as the powder charge is increased? If so its burning the powder.
I would then point to the 1st Ed. of Lyman's BP loading manual. Note the charge weights for the PAINFULLY slow C&H basting powder grind powder they were using. 180 gr to 200 gr in 54 IIRC (not going to bother looking it up) and ti was still adding velocity.
I have shot 65 gr of FFF in a 32 caliber in a building over white sheets, no unburned powder. I submit that this is a longer powder charge in the barrel that 140 gr in a 62.
NOW with a wet shooting patch it IS possible to have some crud on the patch when its picked up and its possible that SOME contaminated powder grains might not burn.
There is always to possibility that this rifle in not properly constructed and the barrel is moving at the breech under recoil.
It could be with the heavy recoiling loads the shooting position is not EXACTLY the same each shot. All to common when its necessary get up, move around load the rifle etc.
The barrel may not shoot better than this.
The barrel may have a sweet spot that it needs to be rested at. I would try the front barrel key/pin location.
Not using a rear bag is a recipe for larger groups since it reduces stability.
Had the barrel been carefully slugged to assure its not tapered in the bore, tight at the breech and loose at the muzzle or tight-loose-tight as I found on a barrel a I waited over a year for? I would have been thrilled if this gas pipe had shot into 4" even once.
Once the the caliber/recoil level gets to a certain point it becomes a major factor in accuracy. The relatively long barrel time coupled with the heavy recoil impulse can cause pretty wild effects on the target. While not a ML my 15 pound 32" barreled 45-100 Sharps (MV 1370) will throw a shot out several FEET at 500 yards if it recoils a little "off" from not having held the rifle quite right usually I can tell when the shot breaks it will be "off".
This is something people do not take into consideration when building a large bore rifle. Plus the typical Jeager FL and probably percussions as well might have rifling twists in the 17-32" range since "one turn in the barrel" was the common formula until at least the 1860s for European/English rifles over about 50 caliber anyway.
This means they would generally not allow a charge much greater, if as large, as a shotgun of similar bore. But when the twist is slowed the powder requirements may well go up significantly. Though I would expect a 20 bore (62) to shoot with 100-120gr of powder unless twisted very slow 96" or even slower. 72 is a very acceptable twist for this bore size.
Finally who made the scope? Look it over CAREFULLY in all respects. Old scopes often have problems loose screws for one and then...
Reproduction scopes made in China or with mounts made there are not all that reliable. I am going through this with a brass suppository gun with a Chinese reproduction scope but in this case I have little choice since the current price on the proper original scope is "high" IF one can be found and its needed to be "legal" for a class.
Dan