Yeah, I've done 3 sisters with sunflower instead of corn.
Cukes might work for the squash part.
Throw in a few pole beans for good measure.
I like the circle idea too, I'm guessing your community garden is exposed to wind; most are.
We all need somebody to lean on...
And some
compost.
But leave a hole in the circle to get in there for your lost cukes. If you don't pick em, the plant may stop producing new ones. Also, don't
water every day unless its 90+ degrees out. If you don't let the sunflowers get a good taproot, they may lodge (fall over like an uprooted tree).
Lastly, a branching type sunflower might not get as tall as fast, but the cukes will likely climb it more readily, and you can take some flowers inside.
I would use a few mammoth sunflower or grey stripe, and a few autumn beauty or similar branching type, randomly sown in a circle.
But hey, that's just what I would do.
Have fun!