Yeah, there's 40 joules in the cap (72 - 32). Doh.
While tidying the lab, I found a promising datasheet-
http://www.powerstor.com have some aerogel based capacitors, they're only good for 2.75V, so you'd have to use balancing resistors (or zeners, I guess...) stop them hogging volts, but an AA size package (14mm diameter, 50mm long) gets you 10 Farads, and a 1/2 length AAA gets you 1.3 Farads. Samples are available at $25 a shot.

Steve