Camera+'s developers tap tap tap must feel my pain, because they recently added this much-requested feature to a new version. Unfortunately, Apple rejected it from the App Store, because repurposing the volume controls could "potentially result in user confusion." Tap tap tap is philosophical about this decision, saying they understood Apple's position and that they hoped they would change their minds in the future. Although a few other camera apps do offer the use of volume control as a shutter release, these were either only available via the jailbreak store or the developers smuggled the feature through under Apple's nose.
However, it turns out the current version of Camera+ (v1.2.1) has this feature, albeit hidden away-- but it's a snap to activate (pun intended).
(Thanks to Dan at UneasySilence and everyone else who sent this in!)