The P38 did have a hot start problem, even though the previous owner (to me) fitted the little black box. I reckon it wasn't fitted correctly by him so maybe worth taking it off and refitting it. Apart from this, is she behaving herself?
Hire a whacker to compress the hardcore then 6 to 8 inches of concrete. Be aware that you will require a water drain or run off to avoid flooding. Some areas now require planning permission if you block/concrete your driveway due to flooding issues.