The core ferrite material is useless ¨C it has a temperature at which its magnetic permeability changes permanently.? You can read about this on the Fair Rite website in a core datasheet.
Curious... Not too much experience with baluns... When they are like this is there a real necessity for replacement? What is the failure mode? windings burnt open or shorting? Some kind of damage to the ferrite core? Winding shorting to core? Or it just looks bad?
I can understand if the burnt enamel coating allows the wire to short to the core which i think could have been eliminated if glass tape were used for insulation.