I have read here that there are a set of contacts inside the wiper motors and they open up over time and screw up timing makes sense to cause the goofy park issue is never right ,
I had similar problems with my truck last summer bought it used, I pulled the motor and wiper arms all at once it easier that way take out a few 10mm bolts and it falls out of the cowl,
I found my motor had been replaced already once it had a huge rebuilt stamp on it, hmmmm, looked on ebay and found a guy parting a truck in Cal, figured it probably didn't get used much in Cal, bought it... . pay attention to where your wiper linkage is indexed to the motor in park postion before popping it loose from the motor!!! anyway popped in a used motor works perfect, I think your wiper motor is worn out.
with as much as I have read on the subject here, Dodge stuck some cheap wiper motors in.