I dusted off the unfinished chassis and finally ran it last night at Drop Inn Racing, in Craigavon.
What was immediately apparent (once I properly screwed the bulkhead on

) was some pretty savage initial turn in, combined with continued 'cocking' of the rear wheel around corner. The flex was severe enough that the car twice popped a driveshaft without anything breaking.
The only remaining way I can see of stiffening the existing chassis further is attaching carbon fibre panels (made from the chopped top deck) along each side using servo mounts. I suspect I'd need three mounts each side (rear, middle and front), but could use just two.
After that it's either 1) get a new chassis cut or 2) get a c4.1!