I'd recommend using a shotgun bore brush - 20 ga, and chucking it in your drill. Spray some solvent in the chamber, then hit it with the brush in the drill. Repeat as needed. Frequently these rifles have old dried cosmoline and/or other gunk in the chamber, which causes this problem.
I kinda doubt you could get a Mosin barrel hot enough to melt the lacquer coating on some ammo; I could be wrong, though.