I disagree. His layup is extremely heavy for a track car. The core is not lightweight, it's very heavy for a core material. It will not compress under vacuum at all - autoclave pressure is a different story of course.
I make race car panels for a living, it's virtually all I do. Any car with panels thicker than 2mm thick is at the back of the pack, that's for sure. All of my race car panels are 1 layer of 240g carbon and 1 layer of 450g carbon and that's it. Hell, some of them are just 2 layers of 240g. Most of them last forever, some of them need to be replaced every now and then - that's mostly splitters that wear through from hitting curbs. Occasionally might get a hole in a side skirt or a crack in a front bumper, but there would be hundreds of laps in between.
I certainly don't use Kevlar in any panel except perhaps the bottom of splitters or undertrays, and thats just to give them a bit of abrasion resistance to get a few extra races of out of them. Kevlar doesnt add 'give'. It holds the panel together when it fails. Realistically, it makes the panel weaker for a given weight, as it takes less energy to break than if that same panel were solid carbon. It is required by regulations in certain race categories for safety, but other than that it is a total waste of time in most amateur level race cars.
Thing is, if you have the moulds then making a replacement panel is cheap when they are lightweight. Especially if you are laying them up yourself and not paying for any labour. Non-structural race car panels should be as flimsy as they can be without the wind speeds punching a hole in them. For carbon panels, that means paper thin.