How can I warp text around a freeform vertical curve?

Hi, I'd like to warp text vertically around a curved shape. The effect is somewhat like the text in the following image.

I've tried Envelope Distort with the Mesh tool but it just doesn't warp the text as cleanly. Also tried out saving the graphic + text as an Air Brush and applying it along a curved path, but it ended up looking slightly flat, as compared to the image which looks almost 3D?

Any help would be appreciated, thank you.