Anyone got an idea if such contract exists and what the rate might be?
Through Lloyds of London just about anything is insurable and some syndicates specialise in 'Special Risks', i.e. one offs etc. You would need to find yourself a Lloyds broker who can conduct business in Lloyds. You are probably looking at something like the difference between 300hrs and zero hrs additional premium, charged pro-rata for each of your flying hours, reducing as your experience increases. The current insurers could well be the ones to approach about this, with the schools agreement.