I use the Lee conical in my reproduction Remington Army .44. Here's what may help:
1. Eliminate the wad. There's no need for it under the conical bullet, if the bullet is properly greased. The only reason for a wad under a conical bullet is to take up space so you don't have the seat the conical deep into the chamber. In this case, seat the wad first before trying to seat the bullet.
2. Drop the conical into the chamber. Rotate the conical a bit against the mouth of the chamber, so the shoulder of the conical rests squarely against the chamber mouth.
3. Using the rammer, apply very, very light pressure to the conical nose. You only want a little resistance of the conical's belt against the chamber mouth, at this point. This often squares the bullet against the chamber mouth and helps to eliminate cocking.
4. Check that your conicals are being cast correctly. If the mould halves don't match, one side of the conical will be slightly longer than the other. Look at the seam on the bullet. If a grease groove or driving band appears higher or lower on one side of the seam, than the other, your mould is not closing properly. Check your mould.
5. Seat one conical at a time, instead of trying to line up 2 or 3 on the cylinder. A greased felt wad seated on the powder will keep the powder from spilling from chambers during handling.
6. After very gently seating the conical, to true its driving band against the chamber mouth, seat it with one, quick motion if possible. A long, firm seating should do the trick.
7. Get a pistol stand for your seating, for those of you who don't have a separate rammer. I use the rammer on my pistols, in a stand. This gives me a better feel for how much pressure I'm applying. Also makes it easier to seat wads and projectiles.
8. Check your bullet alloy. While you might get by using wheelweights for cap and ball sixguns, it's a rather hard alloy. Use the very softest lead you can find. Pure lead, if you can find it.
Can't think of anything else. I shoot conicals once in a while but mostly shoot balls. Never found conicals to be nearly as accurate as a ball. However, like yourself, sometimes you just feel like tinkering with conicals.