Skinning the whole thing is a possibility and the resin that EC sells is a good product to use

However, skinning is quite labour intensive when is comes to the finishing work and achieving a really good finish on larger parts can be difficult, unless you're thinking of only flatting things to a stage where you can have it professionally clear coated. There is also shrinkage of the resin to consider, especially on a part that will be exposed to plenty of sun so, ideally, you'd need to think about giving it an elevated post-cure to speed-up that process and it'll give you a more resilient resin surface to flat and prep. Added to that, you'll be adding a bit of weight and it might be desirable to lose a bit if the car is track-focused?

Unless you're minded to proceed with making a mould of the whole thing with a view to creating a carbon fibre copy, then perhaps you could think about replacing the main section with a carbon sheet and just skinning the side sections? Overall, though, the general shape doesn't appear overly complicated and it sounds like you have the design skills to create a supporting structure for the underside, if adding more strength to the roof is needed (have you a roll cage fitted already?). Perhaps some elements of the side sections could also be retained and bonded back in to provide the necessary fixings also? 

I only suggest this as with the stripping-down that you've already done, it looks like you're half-way to a mould-able original, so it seems that you'd only need a reliable coating on it to think about adding flanges and creating a mould?

Just a few considerations, but I appreciate that skinning can sometimes feel a bit of an easier route to achieving the cosmetic look you're after. As an initial project, skinning something of that size can be a bit daunting, though, so it'd be good to experiment on something a little smaller, initially, just to get the feel for it. Things like getting the edges neat without compromising the fit can be difficult, for example.