Wrap text into semi-circle region

Question

I'm modifying this glass button code to allow for both a Text and a TextExtra property. The goal is to render the Text in a larger/bolder font on the top half of the button and the TextExtra in a smaller font on the bottom half.

I'm having trouble finding a good way to do this when the button is round. As written, the code uses the text rendering of it's Button superclass, which works fine even for a round button with just the Text property. I assume I'll need to render the Text and TextExtra myself, but can't think of an elegant algorithm to wrap the text into the semi-circular regions.

Any approach/pointers welcome.