The first thing I would do is remove all the grass from around the base of the plants and put down mulch. This will greatly reduce the number of pests. Then to get rid of any and all insects that are on your plants I would spray with a spinosad product.
I agree, mulch away that grass. Other than that nothing else, sunflowers are tough and short-lived plants and the most important thing they need, besides a little water is sun, sun and more sun.
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