You can actually do this in illustrator. The trick is to make sure that once you use mesh tool you drag the along handles back to 1/3 of the way along the edge otherwise it squeezes the image along.
Image 2: Getting a even distort along when the shape gets shorter
In addition it can help to keep rotating the are back and forth, for easier selection.
Image 2: doing the scruple
Tough there are better tools for this, it can be nice t know this for other purposes that may arise.