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Spring or fall, after they're done blooming is optimal. However, I have done them in the summer before. I just cut them way back and water profusely. (Which I hear won't be a problem as you have had so much rain. Meanwhile, my lawn and plants are quite brown.)
My mom brought me purple cone flower and black-eyed susans about a month ago, along with hollyhock and batchelor's button. All we did to help them along was to be sure and transfer all the surrounding dirt along with the plants (so as to avoid much disturbance of the roots) and then water faithfully each day for an hour or so. At any rate, I'm sure the middle of summer isn't the ideal transplanting time, but it worked, which tells me they're pretty hearty flowers.
Agreed -- all of those are pretty hardy perennials. Fall works, but personally I typically move them first thing in the spring after they pop up little sprouts. They hardly seem to skip a beat that way and will be as big as if you never moved them.Happy gardening!