You have multiple issues that need to be addressed.
First, your rifle needs to GROUP. Group size is most affected by load, sights and trigger. I would fix the trigger pull first. A heavy trigger that is crisp and consistent is ok, but "very heavy" will interfere with your ability to break the shots in the same place, even off a rest. By the way, rest your rifle with your hand between the fore end and the rest to minimize barrel jump. A rested rifle will shoot higher than an offhand hold.
Next you should work on your load. First thing to know is your bore size. I believe Parker Hales are stamped under the breech. I would believe you can trust that marking for starters. If it's not marked, buy some minus bore gauges from Travers Tool to verify what you have. A "minus" gauge is .0005 (half a thousandth) under size so a .577 gauge will be an actual size .5765 that will be a snug fit into a .577 bore. These tools may cost you up to 5 bucks each, usually less, but will last you your skirmish career. I bought ranges of gauges around all of the common CW calibers (.515, .535-.540, .575 to .581 and .678 to .690) Sounds like a lot, but you'll waste a lot more money chasing group sizes.
I would try as many different bullets of the proper diameter as you can. One or two of those will be your magic bullet. Look for a sutler called CWBULLETMAN (I think). He advertises cast bullets for sale so you can get a small quantity of the common minies (500 gr Old Style, Lyman 575213 for instance). Shoot the heavier bullets with 40 grains of 3f to start and then with 5 grains more or less. Many shooters try 1 or 2 grain increments but in my experience, and for shooting offhand and at the distances we do, 5 grains is good enough for starters.
I size every bullet I shoot for two reasons. Sizing trues up the roundness of the skirt and removes excess lube that can affect loading. I use my own lube recipe in a Lyman lubrisizer with a custom base pin in the sizing die that presses the skirts out to the correct diameter. Many use a push through die with good results but that's not my style.
After you have the right load that groups, fix the sights. Once you have the front and rear sights reworked to give you a consistent sight picture (leave the front sight taller than you need it), you can calculate the needed corrections by dividing the sight radius by the distance to the target in inches. For example, lets say the distance from the back of the rear sight to the back of the front sight is 27". To move your group 1" at 50 yards, divide the sight radius (27") by 1800 (50 yards x 3 feet x 12 inches) and you get .015". For each 15 thousandth that you add, remove or move your sights right and left, your group will move 1" @ 50 yards. Save this calculation for future use as well.
This advice is what works for me. I'm not the top shooter on the line, but my guns hit where they are pointed, which is what you need to get to the next step.
Bob Anderson
Company C, 1st Michigan Volunteer Infantry
Small Arms Committee
"I won't be wronged. I won't be insulted. I won't be laid a hand on.
I don't do these things to other people, and I require the same from them."
- John Wayne in "The Shootist", 1976
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