I tin the barrel and rib with acid flux, steel wool and lead solder. I work my way along several inches at a time. Once everything is tinned I wash it well and coat it with liquid rosin. I then assemble it all with wire and wedges, c-clamps, and a steel ramrod. Once I am situated I melt the solder, working my way down the length several inches at a time. I use one propane torch in each hand.
I don't see how putting a hot rod down the bore would help anything. I am not understanding the value of melting all of the solder at the same time. The chances of movement would be much greater. Most of the trouble with soldering is from over heating, not under heating.