Hi Meadow 1, I rcommend a sharp spade to slice down and cut dock roots about 6 inches below surface level. In my experience they either do not re-grow, or weakly so another incision eg with trowel will weaken the parent root and then they give up.
If you had done that last year,nit would have been easier, always worth taking all necessary precautions in first year.
After removing roots, maybe poly/ tarp over the top until late summer: grow potatoes or squash through holes.
Don’ put membrane down with soil or compost on top, you are poisoning soil,nstopping movement of worms etc.
Be thorough!
