Normally you would dry your onions outside but I can quite see that the weather can make a bit of a mockery of that idea. They need the sun but they also need to have an airflow. Once they have well and truly dried, they will store in open weave nets. Some types store better than others too.
I rather think your G/H may be too damp an atmosphere to dry your onions off properly and once they begin to grow mouldy, they will just continue to rot.
Other than taking all the onions on a winter holiday to somewhere dry and sunny, it may be that you should just use them now and chalk it up to experience.
You can make all sorts of things with them ( sauces, preserves, soup, etc ) and pop them in the freezer.
Sorry not to be more encouraging
That's a pity dambuster but at least they aren't a total waste if they are adding to your compost. Not quite as tasty tho . Better luck next year.