Envelope distort may not get there accurately enough for the finished product but could be a good start.
On the other hand, tracing by hand with the pen tool using the image as a template might be a good way to go. You'd really only need to trace one instance of both words, and then copy and paste and rotate the others into position and tweak if necessary.
Time-wise it may be six of one and half a dozen of the other. I suggest playing around with it a bit to get a feel for the approach you like the best. 🙂