If I understand you, the sides of the hing where you intend to put screws is where I drilled the holes for the pin. Believe me, if it'll hold your screws, it'll hold my pin.
It really should work. From your photo, it appears that the hinges I repaired are the same design as your Dual hinge.
The finish nail passes from one side of the hinge to the other through the hole that you drill through the plastic. It
will hold.
I played with your photo a little.
View attachment 666537
Above, you'll see the red lines. They correspond to the cuts you need to male to open up the space where the pin will go. (Really, you don't
have to remove it. It just makes it a helluva lot easier to push the spring back into position before inserting the pin/nail.)
The green line is where the pin will be. Drill the holes in the sides of the hinge along that line and maybe 1/16" to 3/32" from the top edge.
View attachment 666538
Above is the photo of the hinge I repaired. As you'll see, it's the same design as your Dual hinge.
John