There is a very nice private strip mid way between Cowes and Bembridge.
I was taken there by friends last year with a view to giving it a try but have not yet done so. It looked in very good condition and very useable.
I havent got any contact details though I am afraid but if you think it would be any help I can try and get a phone number. What length do you need?
Mind you as you probably know it is really easy to get a taxi at Bembridge (a call on the radio in bound works) and Cowes is not that far.