Normally you would just connect a wire from the data out connector on the end of one strip to the data in connector on the next strip and so on. That way, only one Arduino pin is needed instead of 4. If the data out connector is not accessible, you have to do it the way you did, but I would expect the data out connector is accessible so that the modules can be daisy chained.
Alternatively, if all 4 strips are to always show identical patterns as each other, all 4 could be wired to a single Arduino pin.
So you have 4 strips of 84 LEDs. How will they be physically arranged? When you light up LEDs in turn, which strip? Should each led fade on to full brightness before the next led begins to light, or will some/all leds fade at the same time but staggered?