The trees on the top E>S boundary will throw shadow longest in the top left-hand side of your plot, according to your plan drawing.
So bottom half in the diagram will be sunniest, or failing that I'd put them just above the frame on the top, right-hand side.
If the soil is fairly free of weeds, I'd just put manure on top and leave it for the worms to take down. If the soil is too soft, after digging, sweetcorn can blow over in a high wind.