Just to be sure I'm understanding the issue: The engine turns backwards when push starting it, but only when the ignition switch is turned off?
I've read some weird stories on internet forums, but this one is in the top ten.
Sir, that's simply impossible.
Marv,
No alcohol but we sure thought about it.
The starter worked fine and turned the engine in the correct rotation...was just when we were trying to roll-start it that it changed direction with the switch on.
I'm going to go through it again just to make sure without doubt it wasn't in reverse instead of 2nd.