I wouldn't use the paper tape as a hinge tape. It might work, but any treatment soaks in and the tape becomes brittle -- fine for an edge, but not so good for a hinge.
Have you tried sanding the packing tape lightly with a fine-grain sandpaper? it breaks the smooth surface and gives the paint more to grab onto.
You might also consider one of the paints designed for plastics, although I've seen a few of those not live up to their advertised "works on plastic"
finally, if all else fails . . . try Blenderm. It's a medical tape that works great as a hinge tape, but it's also a bit more textured. It's harder to find in brick-and-mortar stores, but it should have a better chance of holding the paint.