I always thought rust was more a dry weather thing, but presumably not. You live and learn - looks like something I will have to look forwards to then!
Is removing leaves to prevent spore propagation or trying to protect the existing crop? If the latter I would suggest doing half and leaving half, then you'll see if it affects the yield.
I did a bit of internet research....
Edible backyard says these things may help:
plant early,
give appropriate nutrition (excess nitrogen can exacerbate the problem),
don't plant all in one block - sometimes one area is affected and another will stay clear,
mulch to prevent soil splash,
spray with competing organisms (seaweed tea) or possibly with milk
practise crop rotataion and leave as long a gap as possible between allium crops
don't compost affected leaves unless you can achieve temperatures to kill the spores.
I suspect you could put the leaves where there are no alliums and it would do no harm - like under a hedge?
I love your picture of the garlic drying in the front garden!