Nick, you could, in theory, come up with a mortarless setup that is not that heavy and can be set up/broken down relatively easiily (once it's cooled of course). I have a few prototypes floating around in my mind.
But that's basically just a box of bricks. A box of bricks, in your own backyard is one thing, but a festival where record breaking quantities of psychedelics/pharmaceuticals are being ingested? 1000 deg. ovens and psychedelics are not a good mix. Insulation and weatherproofing provide obvious energy efficiency and moisture prevention, but, less obviously, they protects anyone that might accidentally brush against the oven. Once you start adding insulation and weatherproofing, though, you're talking about an exponential increase in complexity and considerable additional expenditure.
For a festival like this, I'd leave the food to the trucks- or to people with grills. A grill is probably not the best tool for an event like this, but it's considerably safer than a mortarless oven.