Steve, for springy round wire, consider a thin bicycle spoke. This material is commonplace and cheap, new and used, in carbon and stainless steels of several diameters. It is fatigue-resistant metal and cold-drawn to pretty decent yield strength while retaining good ductility. At locations of tight bends where springyness is not needed or wanted, you can anneal the wire with a candle flame and then make tighter bends.

It looks like your spring action is like the spring in a clothespin, but with only part of one turn in the coil, and with more reliance on bending in the arms. If you can wind in several tight turns at the hinge it will soften the action. If necessary, you can hammer the round wire flat where you need more flexibility.

Another configuration is to have a round wire torsion bar running parallel to the hinge axis along the door lower edge, just inside. Crank the ends 90 degrees as needed. Gas welding rod, or brazing rod, in small diameter is another cheap source of springy wire.

Rain? Out there? Congratulations!

C. O. Greenlaw, Sacramento