1987 Chrysler LeBaron GTS 2.2 auto gas pedal issue

Dead engine and transmission mounts. Engine moves against static load when trans is put in drive -- excessive engine movement pulls accelerator cable taut, causing the stiff/binding feeling. Punching gas causes engine/trans assembly to move further, which pulls shifter cable taut and causes inadvertent shifting.

You should check for broken motor mount(s). May I suggest starting with the poorly designed mount at the frontmost lower area of the engine compartment? Excessive powertrain movement can cause cable operated devices (gas pedal and shift lever) to move or bind. If you're unlucky, even an axle shaft may fall out with significant transaxle movement.

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