I'll bite... I'd say no. Maybe an OLD custom job. Never seen one like that, but not the definitive answer. I'd be curious to see if it's black or green under the body molding or under the door handles. That might give you a better idea but I'd still say custom.
I like it...It's different. Reminds me of the Mopar Missile cars. It's cool because it goes well with the side molding and the indentation that runs from the fender to the quarter panel. If it were me and knowing it will cost just a little extra when repainted...I'd keep it for sure.
The only stripe I've seen on 4-doors from the literature is a pin stripe, much as you have at the top of the area you describe. Ultimately it's your car, do as you wish.
IMHO, keep the stripe, though I'd prefer it in the color of 70DartMike's car than black. As others have said, it looks good, distinctive, and is not over-the-top.
I would agree that it is not factory, but honestly I think I have seen that paint job in person on a 4 door a-body before. I've seen your car before on this site and it always looked familiar to me.