Hi there,
First at all (indeed) you have to get rid of almost all metalic parts and replace where necessary with proper materials (al, carbon fiber, rubber, etc).
The most important is to keept the core(main longeron) low weight (like an profiled Aluminum tube) which to give it resistance and lower torsional shiftness, on which to come up with other elements.
Second - you have to lower the weight of the transmission - use synchronius belt and pulleys, or change to cardanic transmission, where the shaft to be made from carbon fiber(it's easy to find such thing and cut it to dimension).
For a better stability in curves, you have to modifay the angle of the wheels, and most likely to have a new kind of joint - see the wheels on Mercedes.
These are few (free) advices. More, if I'll win the bid. Anyway, meanwhile you may send me some drawings and I could take a look.