Use latex tubing instead of rubbber bands. People have made water balloon slingshots that stretch for over 10 feet this way.
Link to water balloon slingshot site, note the babes in the drawing look a tad better than the guys in the actual photo below.
http://www.slingking.com
Latex tubing is also used as the tension source to lauch radio control gliders similar to a person launching a kite, and you can get stronger strengths for a shorter pull / more tension:
Here's a link to one source of latex tubing of various strengths:
http://www.aerofoam.com/hosemonster.html
and a link to the former distributor with some actual data:
http://www.hollyday.com/rich/hd/sailplanes/rubberdata.htm
I've stretched the rubber to 350%, a bit more than shown in the graph.
At 350%, the heavy duty tension increases from 24lbs to 27lbs. This is now
called the "4 meter unlimited" at hosemonster.
For my radio control glider, I use 60 feet of the heavy duty / 4 meter unlimited, with 210 feet of monofilament fishing line. I pull back 180 (300%) to 210 (350%) feet for a launch. Here's a video of me with an Artemis Light, 10'2" wingspan, but only 4 1/4 pounds weight.
jrartms.wmv