Help with complicated product setup

I could use some advice on the best way to set up a complicated product. I need to list a product that has many different options that need to be populated by preceding choices. For example:

Product: Stratocaster Guitar Body
- Construction: Solid, Hollow (+$50)
- Wood Type: Poplar, Alder (+$30), Mahogany (+$50), etc.Some wood types not available if Hollow Construction selected
- Top: Flat, Carved (+$50)
- Binding: Black (+$10), Cream (+$20), Ivoroid ($50) Only available if Caved Top selected
- Color: Black, White, Red, Yellow, Tint, etc. Certain colors only available on each Construction, Wood, etc.

I'm guessing that there is no way to set up a product to work like this in Magento. Would the best setup be to add each of these Options (Construction, Wood Type, etc.) as a Configurable Product with the selections? Could I then have a product that has groups of Configurable selections?

Or, would I have to use the Magento API to create a separate page, pull the product data and create a bunch of drop-downs that get populated via AJAX instead?