I think what you would want to do is reduce the amount of fat in the recipe, as there is no way to get fat to dry out (well, except by using n-zorbit). Maybe use more cocoa powder and less chocolate, and skip or reduce any butter or other fats. Add more water or skim milk as needed to get a spreadable batter. Then proceed as you are currently doing, baking it as thin as possible. I would aim for a longer time at a lower temperature as that will produce more even baking, instead of only crisp at the edges.
As you noticed, white chocolate doesn't have the same fat or solid makeup as regular chocolate, and in baking that will make a huge difference. The proportions of starch/binder (flour) to fat (butter & chocolate) to protein (eggs) are what make the difference between cake, brownie, fudge and everything in between.
White chocolate tends to melt faster than regular chocolate, so the baking time will be shorter, and there'll probably need to be extra flour & butter to make up the difference.
Go ahead and google for a basic recipe & then you should be able to make most of the same add-ins (nuts, extracts/flavorings) as any regular brownie recipe.
I would warn you to stay away from the "marble brownie" recipes though - they're really popular, but these are not two batters that play well with each other.
EDIT: Regular chocolate varies broadly in its fat makeup - different countries have diff regulations on what types of (natural) fats and (artificial) emulsifiers can be added to chocolate and chocolate-derived products. White chocolate has the same ingredient list as milk chocolate (w/o the cocoa solids), but again, the proportions and allowed/disallowed additives may be different. So you have to mind your brands/country-of-origin, as well as the "family" of chocolate.
Hershey's (US): http://www.thehersheycompany.com/nutrition-and-wellness/chocolate-101/types-of-chocolate.aspx
EU standards: http://europa.eu/legislation_summaries/consumers/product_labelling_and_packaging/l21122b_en.htm (If someone can find a more consumer-friendly explanation of EU chocolate labeling, that would be great.)
Best Answer
One of the most important factors in achieving a fudgy, chewy brownie is cooking time. Essentially you should be slightly undercooking the brownies so they don't dry out in the middle.
Use the cooking times given in recipes as a guide only, because each oven will vary. 5-10 minutes before they 'should' be ready, start testing the centre of the brownies with a toothpick or cake tester: unlike a cake, you want a good amount of sticky crumbs on the skewer (but very little liquid batter). Remember that the cooking process will continue even once the brownies are out of the oven.
Another factor that contributes to chewiness is the sugars you use: adding some sticky, dense, dark sugar will help create a fudgy brownie. The brownie recipe I use, which is pretty damn good, uses 1.5 cups of granulated sugar and .5 cup of packed dark brown sugar.