Warping skewed type on a path

Hi,

As you'll see in the attached screenshot, I wanted to type along a path that mimmicks the marquee in the photo that is in the background. I was able to get it to do that pretty easily by just drawing the path, type on a path and then type on a path options/skew. The only slight thing is that the last couple of words start to curve back out when I want them stay against the marquee rail.

Is there a way to warp it in InDesign?

Or would it be easier to do this in another program?

Thanks!