Danny,
Yes, transverse leafsprings are definitely a feasible and potentially good idea for FSAE (ie. lighter, more integrated...).
As noted above UWA used them for quite a few years integrated into their lower wishbones. The more radical UWA-2012 car had 2 x composite "W" leafsprings acting as both springing and location of the chassis to the unsprung undertray/beams/suspension.
Many production cars from the 1930s to about 1970s used them, mainly for front suspension in Europe, but at rear first, then all round (and still?) on the Corvette in USA. (My late-1940s Tatraplans have double-transverse-leafsprings (acting as wishbones) +R&P at the front.) Doug's Wiki link covers the pros and cons quite well, including Carroll Smith's positive endorsement.
For kinematic calculations, a cantilever leafspring (ie. clamped to chassis at one end) that is "L" long has its outer end travelling in an arc of radius about 3/4 x L (ie. it acts like a slightly shorter wishbone).
For material you could use Glass or Carbon Fibre Reinforced Plastic. Glass FRP has significantly better strain energy capability than good quality spring steel (ie. lighter for given load-deflection, or energy-storage, capability). Does anyone have the numbers? Have a look in Archery stores for inspiration, or watch "Arrow" on TV.
Glass FRP "pultrusions" (fibres dipped in resin then pulled through a heated die) are widely available in many different cross-sectional sizes. These often used for things like stiffening-battens for yacht sails. These would have to be machined to a taper for less weight and more even stress. Or you could lay-up your own from "rovings" + epoxy resin...
For tuning of spring-stiffness effects on handling (eg. LLTD) you could make the main transverse-leafspring/wishbone so that it is at the softer spring-rate end of the expected range, then add extra leaves on top of the main leaf to increase the rate (ie. like a conventional stack of leaves...). Or many other ways...
A Swing-Arm suspension with transverse leafsprings would be very simple, low parts count, low CG, low cost, rugged +++...
Z