If you have a CC version of After Effects you can do this with Cinema 4D Lite (included with AE CC). It will be a bit of a learning curve, but well worth the time.
Basically you’ll create a Plane and modify it with the Bend Deformer. You can use Bend Deformer’s coordinates and falloff to get the desired effect.
You’ll have to learn a bit about C4D workflow and AE integration before taking those steps, but once you’re there it will be pretty easy.
If you twirl down your text layer you’ll see an Animate option just to the right. Select the Tracking option and then keyframe the Tracking Amount to your liking.
In your AE file drop-down menu there’s an option called “Collect Files”.
You can use this to gather all of your current project assets (including the AE file) into one folder on your hard drive.