I rarely use cloths, just a sponge with light scrubby stuff on one side and microfibre on the other. Very neat.
When I do use cloths, (I do occasionally need them now too!), I got an over radiator airer and put it on top of the fence just outside the back door. All the bits and bobs went on there after rinsing out. And I put a suction hook by the sink for a dry clean one.
Maybe get smaller cloths??