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This sounds similar to the Electrathon racers that compete locally. Those are limited by battery weight, not number. What are the battery dimensions?
Electrathon racers tend to have stiff, if any, suspension and a thin noisy body that rattles as they go by. I would consider Polymetal. It is stiff and would make for a rigid moncoque, but would favor simple curved surfaces.
The 'almost three-wheeler' design could be built with 4 wheels, even enclosed. The rules sound like they would permit a narrow rear track, like an Isetta. The basis is that the body can be constructed from triangles, diamonds or hexagons. Each edge is mathematically defined to whatever precision you can cut to. If it's flattened into a 'peel pattern' it could be cut out of a flat sheet with the darts cut as overlapping tabs that are riveted or spot welded. Sort of a quasi-compound curve.
I will now wait quietly for your pictures.
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