The description of the internals of your speaker does not fit all. Many use quality binding posts, soldered internal connections, etc... Maybe it's time for some upgrading.
As for the thickness of voice coil wires...try using that wire from your amp to your speaker terminals or vice versa, replace the voice coil wire with the heavy gauge wire that you're using from your amp to the binding posts...let me know how that works out for you.
As for the thickness of voice coil wires...try using that wire from your amp to your speaker terminals or vice versa, replace the voice coil wire with the heavy gauge wire that you're using from your amp to the binding posts...let me know how that works out for you.