Another classic way of increasing the in car exhaust noise is folding the back seats, which I used to do in my supercharged XF. That's obviously not an option in the F-Type but the corresponding thing to do in the F-Type coupé is to remove all the loose unnecessary trim parts in the boot.
Before a properly spirited drive I remove the big boot cover, the smaller one on the boot floor, the cover that sits over the battery and the under boot compartment trim piece. That eliminates most of the insulation between you and the exhaust, makes quite a difference and gives a much more unfiltered exhaust noise in the car.