I wonder if the way round this is to make contact with an owner of an FAA registered aircraft here in the UK? There are around 200 such aircraft over here with the Cirrus SR20/22 being the most numerous. Equally there are a number of high end Biz jets - how's your G6 type rating
But there are quite a number of Pipers and Cessnas around - my own field has a C182 based for instance.
Place to ask is
https://forums.flyer.co.uk/viewforum.php?f=1 along with this thread.
Or just ask Sam Rutherford......