There are dwarf varieties that will stay shorter, but there are numerous plants with smaller flowers and large plants. They thrive in full sun. I love to grow various species of sunflowers. But, in the past I have started them inside and put them outside when they are about six inches tall, and bugs have eaten them down to where they are about one inch tall. I am desperate.
Animals love tender, new vegetation.
You have several options. One is to start some plants indoors for early planting, and then plant new seeds every two to three weeks outdoors after all chances of frost have passed. When you put out the new seedlings, use a protective covering until they become well established options include floating row covers called Remay, milk cartons or jugs or even fabric netting. If it is insects, you can also use insecticides if you know what is at work, or the Remay will help to keep them out. Hopefully, once they become well-established, you will have less problems, and will be able to enjoy the resulting flowers.