Life as a Product Design Intern at Khan Academy
elizabethylin.com
elizabethylin.com
And the portfolio site in general is really something else. You should definitely be more than an intern!
But, if they don't than I'm 100% with you. It's better to work on something worth doing for less money, then work on something you don't feel passionately about for more.
I worked for a guy for nearly 4 months at a sub-par pay. That work turned into an opportunity that brings in six figures every year.
I understand where you're coming from, but sometimes, you have to give before you can get.