Starter stays engaged ONLY in park???

Did you correct the A1 (battery) wire connections?
I ask because this is critical.
Now the question is WHY did it get so hot that it melted to those wires? On to the interlock connector in the cabin of the car.
And we could also ask whether the damage to the R6 wire relates to the missing fusible link?
Did somone just hack it out for the fun of it? I doubt it.

but I think I found what 67Dart273 was referring to regarding the connector. See the blue connector here.
Nope. Look at the wire insulation colors.
I'm pretty sure I know what it is, but best you look it up in the book.