One note about sunchokes, one season of mowing killed my 3-year-old patch. Mowing was assigned elsewhere, and they were gone when I thought to see how prolific they were that early fall. So, if they aren't actually in a bed, not quite so unkillable. The patch had been 4 feet wide by 30 feet long.
Pole beans will probably do well, but you could also try yard-long beans, they take a bit longer to establish but are worth it. Also sweet potato foliage (the rabbits LOVE it), trained up to climb onto something. If not, another vote for loofah, they are AMAZING and plus you get free things to wash your dishes with when you rip them out.
I wouldn't think that summer squash would grow tall enough to shade a lot. Cucumbers might, but where I live they (and summer squash) get powdery mildew and die nearly overnight, and that would stink if it happened early in the season and left you without any coverage. (when I had the mildew disaster early this spring, the loofahs were totally free of any mildew, even though the spaghetti squash and pumpkins were affected too. The greenery has a really strong smell, maybe it has some sort of loofa magic that makes it immune).