Scratch cakes using fresh fruit usually don't have batters heavily flavored with extract in the same fruit flavor so that the actual fresh fruit can be the star:

http://www.foodnetwork.com/recipes/paula-deen/grandgirls-fresh-apple-cake-from-georgia-recipe/index.html

http://www.epicurious.com/recipes/food/views/Apple-Bundt-Cake-102692

http://www.food.com/recipe/apple-or-pear-cake-98869

http://allrecipes.com/Recipe/fabulously-sweet-pear-cake/detail.aspx

http://www.bbcgoodfood.com/recipes/2414/fresh-cherry-cake-with-a-hint-of-cinnamon

http://www.joyofbaking.com/CherryCake.

It almost seems too obvious to advise that you can always up the strawberry flavor by using strawberry extract instead of, or in addition to the extracts recommended in this recipe.

Or you can simply use your favorite pound cake recipe and flavor that with as much strawberry extract as needed to get a strong strawberry flavor (without using any fresh strawberries).

I would prefer Ryan's recipe... where the natural flavor of the fresh berries is highlighted.

HTH

I hate to disagree, but the above Paula Dean recipe has only one 3-star review. In addition, it uses AP flour (which the OP asked not to use) and 3/4 cup of fresh strawberries.

Ryan's recipe is so much closer to Grandmother Paula's sour cream pound cake recipe which I linked to and which has 343 5-star reviews. Both Ryan's and Grandmother Paula's recipes use similar amounts of ingredients and both use cake flour. Only big difference is that Ryan's recipe adds 2 to 2-1/2 cups of fresh strawberries.

HTH