I have tried practically every last method known to make a high performance supercapacitor I can use in my power armor, prosthesis, and space planes.

I think I finally figure it out and it should have been obvious but it wasn't. Batteries must have very thin active materials very close to each other because of how they work. Ions such as lithium has to travel all the way from the anode to the cathode when discharging, so rate capability (c discharge rating and charge rating) is impacted by distance. However supercapacitors operate completely differently. The charge is stored directly on the active material and faradaic redox reactions at the cathode only occur at the cathode, meaning no ions have to migrate all the way through an electrolyte.

This means as long as the active materials for each electrode are conductive enough to not cause ohmic losses through resistance they can be incredibly thick. Illustration below

I finally got the materials in today to remake my forge, it's a little too hot at the moment to run the fireplace so I can proceed.