I do lots of transplanting of sunflowers, and have never found them tough other than when
root balled or have not developed
enough roots. I usally start a cold frame with them broad casted, racked in with lid cracked to allow some breeze or they get leggy. When transplanting I move them like a sod clump with a shovel. Pre
water plant and fill hole with water allow to drain, break off transplant, water them in... no problems. Hot sunny day not recommended. I usally space foot apart. I have grown them the last ten years just like this. Also in the fall when birds start feeding off the flowers, remove have eaten head place in any location you wish to have volunteers the next spring.
Experiment, invent, build, grow, share....lead by example people!!!