You've got to be careful shooting conicals. They start out tight at the muzzle but get much looser as they are rammed down the bore. Then the bullet & pellets can slide up the barrel too if you carry the rifle pointed down. While this might not have happened with the REAL bullet, if it does you can ring or slightly bulge your barrel and ruin it's accuracy.
So a rifle carried around hunting after it's loaded with a conical can be risky. It often needs to be carried with the muzzle straight up in the air to help keep the load down in the bottom of the barrel.
You're probably better off with sabots if you can keep your barrel clean, but why put a lubed patch underneath it? A very, very thin coating of bore butter part way down the bore after the sabot is loaded may be an option to increase accuracy consistency of the first shot if necessary
, but when it's really cold the lube can get stiff and increase pressure if you use too much. Try a clean barrel first since sabots load tight, and swab as often as possible so you don't get a bad crud ring. Maybe you can use the conical for easier loading if you need a follow up shot in the field without swabbing. Even a small piece of balled up newspaper can be used as a homemade over powder wad. Just don't make it too tight and flatten it down in the bottom of the bore before ramming the conical. It might create some burning embers after firing so try not to start a fire in the woods.
TC makes a new solvent just for cleaning 777, and the 777 pellets are said to burn dirtier than the loose powder. It can also recoil harder.
Is there any way to use a nipple pick on your #209 nipple between shots to help keep it clear?