Hello Ros,
I have not grown indoor courgettes for a long time, had a favourite variety in the eighties called Early Gem F1 and am pleased it is now available again at EW King. However I do not know how it would fare indoors. I did grow Parthenon two years ago and the fruit are attractive and tasty; it is indeed parthenocarpic, somehow able to set fruit without pollination by insects. But I never had that problem, and as you are a demonstration garden, whey not try an ordinary variety in the tunnel to find out how busy your insects are? It sounds like they are active enough.