I wouldn't attempt that with a MIG machine.
TIG would give you the control and shielding you'd want, but you'd need to be concerned with the heat affected zones around your filler/repair.

Have the barrels X-Rayed, multi-pass at different depths, to see how the pits affect the meat of the barrels, also to see in between the ribs for excessive rust/erosion.

Have those barrels been hot-dip blued?

Cheers
Tinker