How do you create text on a path and constrain it to a shape?

I've created the shape below, and I want to put text where you see the red lines. Not a problem, but if I want the text to go from big to small to fit the shape behind it, absolute nightmare. I've tried everything I can think of and I can't find a way to get text to follow the red line and go from large to small.

If anyone has any ideas I'd really appreciate it.

Here is my shape:

I've tried stacking warp effects (one vertical for size of the text, and another horizontal for the arch) but it gets really weird the moment you rotate the text (Maybe there is a way to apply a warp effect based on an object's local axis?).

I've tried running the text on a path (the upper red line) and then using a smaller copy of the background shape for Object»Envelope Distort»Make with Top Object but it is really weird too.

I'm fairly new to AI so maybe I'm missing something simple.

Thank you,

Eric