Shipkiller,
Great write-up and I think trailering the wheels and other parts is a better solution than trailering the car.
I've been considering doing this myself for some time and also been looking into fitting a front splitter and rear wing, for track use only. Once you have made the decision to fit a tow-ball to the car, it occurs to me that it is then possible to use this as a mounting point for a large rear wing, which is placed behind the car so that it will create some serious rear downforce.
It also occurs to me that a simple tow-ball mounted bike rack could easily be converted to become the carrier of a rear wing rather than bikes. There's a very simple but effective design of quickly attached bike-rack that looks eminently suitable for quick and secure fitting, which shouldn't create too much drag from the framework and this is the Thule 970 Xpress and here's a link to a demonstration of it:
I just thought I'd share the idea with you.