I know I don't have any sources on hand right now, and I'll find some later.
Surgical tubing is generally the most powerful springy stuff per length of material you can (cheaply) get. I recall a Mythbusters episode where they load tested various springy materials and surgical tubing outperformed bungee cords of various lengths by a lot. In Overdrive it was pretty much the perfect material, since you only needed to get the ball somewhere over 6 feet high and this far, and other than that it didn't really matter how hard you hit it once you got past the minimum threshold for success.
Springy material is limited by the amount it can stretch without binding or breaking. A good, safe number for surgical tubing is about 5 times its normal length if I remember correctly from random testing. Surgical tubing wears over time and with repeated use which makes failure easier over time as well. I don't know as much about bungee cords, but material deformation is less of a concern as far as I am aware.
Considering that for many kicking styles, shot distance tolerances may only need to be within several feet of the target distance depending on your goals, surgical tubing may work for you. My team has prototyped with surgical tubing with success. Many long range kicks may just need to "get in the zone" rather than in the goal, and the range of force imparted on the ball that will get it in the goal (lowest being barely rolling in, highest being barely not bouncing out) is surprisingly large. Play with the math and see what you get.
http://www.primelineindustries.com/tools.html has a surgical tubing spring calculator assuming ideal (new) tubing at room temperature.