My magneto is a BTH KC1:-
The usual cause of magneto demise is the condenser which is buried in the armature. One remedy is to fully strip and rewind the armature along with a new condenser, or you can snip the old condenser out and fit an external one. This is my plan. Fit one of these:-
Still got to strip part of the armature but hopefully this should fix the bad starting.
More to follow.