Envelope Distort

Jenny,

For the true old fashioned vintage look you may consider the old fashioned manual drawing mentioned by Monika.

We had a rather complete set of exquisite old threads describing such ways covering all sorts of shapes, including some that corresponded exactly to your sample.

Unfortunately, a few years ago we lost two thirds of all old threads, including all of those.

One (dis)similar case was covered by this thread, and it may form some inspiration if you wish to dive into it; as you can see, it is about a rounded bounding shape, and mentions chevron shapes as in your case.

https://community.adobe.com/t5/illustrator-discussions/how-can-i-keep-top-third-of-text-untouched-while-curving-bottom-half/td-p/12186490

See Monika's answers (and video) in this post:

https://community.adobe.com/t5/illustrator-discussions/envelope-distort-text-distortion-problem/m-p/12535336#M299272

Be careful: not Gradient mesh but Envelope Distort > Make with Mesh. This way is more flexible than making with Top Object.
Could you try to create the Envelope Distort with mesh, try to move the mesh nodes, and show the result? Also, will be helpful if you show a sketch of what you want to achieve. In this case, we could say more about the best way.