1960 Valiant moves when pushbutton in ‘N’

I do try to move from the simple to the complex. I figure if Motors recommends doing everything to avoid removing the transmission then that's good enough for me.
External first... ensure the Park and Shift cables are correct... then consider kickdown band adjustment... then pressure checks before dropping the pan for air and clutch checks. The end result might be the same but you'll have a more targeted approach on the repair.

Good luck..

Let us know what you decide to do