I think the time differential has us out of sync! LOL

I was thinking of your ELS as the driver to shape the teeth of bar stock chucked in a lathe as seen in the Haas video. In that case the lathe would need an indexing plate and someway to lock the lathe spindle, or as you indicate, incorporate a stepper to do the indexing and it would be strong enough to hold it. There is no rotab attached to the lathe.

The tooth profile I was discussing is the Gates standard timing belt as show in the Haas video. Here is a screen shot from the video.
Click image for larger version.  Name: Screenshot 2024-03-24 013432.png  Views: 158  Size: 257.9 KB  ID: 47256

However, your sketch looked like the old HTD style that I remembered and that caused me to look for other "standards". Wow, I didn't realize there was so many un-standards today! Lol Here is a link that I think covers most of them.

Anyway, many thanks for your patience and help. I now understand exactly what you are doing.