Mutant Courgettes

It's official. My courgettes are mutants. The little sods have been producing flowers now for a good few weeks, but so far not a single female. The ones that I thought might be female (on the grounds that the stems were a lot thicker than the obviously male ones), I now realise were in fact mutants, where two male stems had fused together, hence the two flowers. An extra gaudy male masquerading as a female? Could be be a cross-dressing courgette?

Exciting though mutant courgettes might be, the dreary upshot is no produce, with the exception of a few stuffed courgette flowers. Stuffed courgette flowers might make a tasty side dish, but they are hardly a hearty meal. Even more irritating, I'm having exactly the same problem with my Patty Pan squashes, which if anything are thriving even better than the courgettes, but also failing to produce any baby Patty Pans. Is this a problem with squashes that other people have met with, or am I just spectacularly unlucky this year?