Uncle Buck, I also have a new Lyman GPH, mine is a flintlock, not sure what you have. Just wanted to share some of my findings. First I found several problems with the quality of the gun. The trigger was terrible like 2 pieces of sandpaper rubbing together, the screw in the center of the metal buttplate was at an angle causing a sharp edge to stick out, both wedge pins were too short (had no confidence they would hold the barrel reliably), and the frizzen would not generate even a single spark (too soft). On top of this I did not like the very sharp edged U shaped buttplate(didn't fit my shoulder) and I didn't care for the very dark and what seemed like a sludgy finish to me.
I went to work on it by cutting off the buttplate, replacing it with a recoil pad, and putting an inlay on the top of the stock where the metal originally wrapped around the top. Refinished the whole stock with a hand rubbed tung finish bringing out the beauty of the wood, it does have a nice piece of wood. Lyman sent me a new frizzen. I replaced the wedge pins with TC pins and ground them back to the correct length.I stoned and polished all mating surfaces in the trigger assembly(now has a fine 1 lb. pull), put on a Lyman peep on the rear and their globe on the front. Here is a picture:

This weekend was the first I shot it. I used 3F 777 and 4F Goex in the pan. Ended with 90 gr of 777 as my preferred load. Used 2 bullets, the PowerBelt 295 Hollow Point and PowerBelt 348 Aero Tip. Both performed excellently. My ignition over 2 days and about 25 rounds was 100% with the 777. Had to clean the frizzen and pan about every 5 shots from the 4F. Had to swap flints a couple times but the 777 ignition was totally reliable. Cleaned the barrel after 15 shots even though there was no need. Last bullet felt the same as the first. Cleaned it with damp patches, 1st patch surprised me by not being all that dirty and the next 2 were quite clean.
The 295HP over 90gr chronied an average 1624fps and the 348AT at 1553. 3 shot groups at 50 with the 295s averaged .90 in. and the 348s were 1.10 in. Group on the left is the 295s and the right is the 348s.

I am choosing the 348s for my hunting rounds as they have excellent downrange energy. I figure this will be a very capable 150 yd gun. This round will still have over 1000 ft lb at 150yd. This is my 100 yard group with the 348s, 2.4 in.

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I am very happy with this setup. I feel ready to go.