I'd read you could transplant them in the fall, after they've died back a bit but before the ground freezes. I finally dug a few out of two local groves and it turns out they're different varieties! My neighbor gave me the okay to plant them (I've been helping him replace his lawn with local plants, and we're emphasizing local food plants in the back). I know they can take over a space a bit, but he seems excited at the idea. He has just about the only bees I've seen in our neighborhood, so he's happy to give them more flowers. And if the sunchokes go too crazy I have a friend who knows how to cook them.
Tucked one in to a sunny spot where someone clearcut along a bike path too. Maybe it'll take off. I've been thinking about trying a little guerilla forest gardening along the path, perhaps starting with edible mushrooms next. I guess they make plugs - you drill holes in dead logs, tuck the mushroom plug in, and you get mushrooms. We'll see.
Awww those purplish ones are so pretty! Makes me regret planting the first random variety I came across lol. They will definitely form an enormous thicket, critters love it!