I used to feel the same way as you about my personality or approach inhibiting my ability to negotiate (another way of thinking about advocacy). There's a classic but very good book called "Getting to Yes." (Fisher, Ury and Patton) Relatively short, available in paperback and there's also a workbook you can use to plan your approach. Reading the book changed my way of looking at these types of situations completely.

I highly recommend reading it asap. A few key thoughts from the book and other negotiating texts.. know what you want/what your alternatives are/what they are likely worried about or trying to accomplish... be willing to be quiet and let them get uncomfortable. (The last bit really creates some interesting situations -- people do not like silence.)