Try as many loads as you can to find the sweet spot. Every barrel is different. What works for one person's rifle won't necessarily work for yours. You can use what other people use as a good starting point, but you need to do the load development to get the most from your barrel.
Load development:
What works for me and how I was taught is when increasing/decreasing the load size is go up/down in 5 grain increments. Also, Only change ONE aspect at a time. Meaning, change only the load size, or the powder type, or the bullet by themselves; don't combine changes! If you change more than one thing and you get a wierd result, you don't know what to go back to, to fix. Make sense? You'll spend more time guessing and wasting powder and lead than getting a good accurate load.
Be realistic about your shooting ability, your max effective range, and your rifle. Some get great results and accuracy out of a ML. Some get fair.
There are a bunch of things you can do with a conical. You can paper patch it like Ron does. You can put a wad between the bullet and powder which can sometimes have positive affects on accuracy.
Powder. Your's could be an anomaly but neither of my sidelocks funciton well with pellets. Recommend sticking with loose powder (but that's me). Don't dismiss black powder as a pariah. I have one sidelock that likes BP better than any of the substitutes. Does it foul more, sure. But for a hunting scenerio I have never fired more than 3 times where I didn't have time to run a spit patch down the barrel to clean out some of the fouling. I can load up to 3 times with a BP fouled barrel before it's hard to push the next bullet down. Once you get a good load worked up, see how many times you can reload with a fouled barrel. This will also give you an idea on accuracy after multiple shots. I feel this goes for any powder, not just BP.
Enjoy the Lyman, it's a great rifle.