Would I not?
My car insurance in the UK covers me driving any UK registered car within the same class of vehicle whilst in the UK, providing that it has a valid MOT & road tax. If it is in a different "class' all I need to do is call them and let them know, they *may* charge me a few quid - but it has never been crazy, even when I borrowed my friend's Porsche.
I would assume, that should I be American, and own a car there, that there would be similar means of ensuring to be insured. Although - of course as a foreigner, you just make sure you take out your own short term policy with a reputable insurance company - that's not that hard to organise!!
Anyway - getting back to the important side of the conversation. The G3 is really cool, and I do want one, but sadly it is way out of my budget! Again - way above standard budget - but there is a company which make "belly pods" for a small motorcycle:
MotoPOD LLC ? Innovative Aircraft Accessories they seem pretty cool!
I mean - alternatively of course, we could by some reliable "old bangers" (ie: £800 - £1000 - cheap to insure...etc..), leave them at the airfields that we use, and reciprocate the "use" of the car for anyone else who is part of the scheme with a simple online booking system.
(probably too easy for anyone to be interested though...)