I have killed 23 head of elk. Big bulls smaller bulls, cows, and a calf.
I have shot them with bows, rifles and muzzleloaders.
Elk can be incredibly tough. I have tracked elk for miles, and I've dropped them in their tracks.
When I'm hunting them with muzzleloaders I use my 50 cal Hot Rod Renegade. It has a fast twist barrel.
I use a paper patched Lee 500S&W bullet. They are 458 grains.these bullets are slightly hardened to between 6 and 7 BHN.
Most factory bullets are poor quality. I shot the 50 cal Hornady 410 gr bullet for several years. I shot only deer with them. While the Hornady is an accurate bullet they are so soft that they over expand. In my opinion that over expansion reduces penetration.
For a factory bullet I would use No Excuse bullets. I have tested them and they shot well in my guns, but itvhas a fast twist.
I have heard good things about Bull Shop bullets but no experience with them.
My last bull I knew I was close to private land. I knew I had to try to anchor the bull. That is a tall order for a muzzleloader. I have yanked the rug on elk many times with a shoulder shot angling back into the lungs, or hitting the spine. Knowing anatomy of elk is important to making good hits.
I held for a high shoulder shot. At the hit the bulls legs jerked up and he was on the ground.
I recommend going for both lungs to guys with little or no experience shooting elk. Hitting a shoulder with a factory bullet or ball is a mistake.