I face a similar situation with sunny windows and fortunately have a green house, but I've found that it's really only beneficial for overwintering some more tender plants. It's an oven in the summer, even when mostly shaded by a mature dogwood. I've had the best luck with propagation trays on our covered back porch. Starting your seeds outside in the heat of summer is probably not the best idea. You'll have to exercise your gardener's patience and wait until spring, ideally.