Was karmic healing accomplished by Christ creating a healing circuit from the divine, through him, to his perpetrators with this famous declaration from the cross?

This was exactly the mechanism involved, which you saw intuitively, that by connecting an act of forgiveness to the perpetrators he was opening a healing circuit to allow Creator’s love to flow through him to them and to create a path for the healing to occur, knowing they would not be inclined to ask for help by virtue of their ignorance of what was at stake for them karmically. Christ, in his benevolence, made a healing request through this on their behalf, and it at once raised him up as well as all of them.