I am using a Canon Rebel T6. I went back and re-read the manual, and I don't think I can reconcile autofocusing and zooming at the same time.
To paraphrase the manual,
Auto Focus during shooting:
"AF is possible during movie shooting using the shutter button, if you enable it in the Menu. However continuing autofocus is not possible. If you autofocus during movie shooting, the focus may be thrown off momentarily or the exposure may be changed. The movie will also record the lens operation sound. During movie shooting, if the AF method is set to Quick Mode, AF will executed in Flexizone-Single"
I took several test movies; with and without AI Servo, and with and without using the shutter button to autofocus, and they all turned out crap. I think my best bet will be to make several, what Canon calls, Video Snapshots of 2-8 seconds each, and string them together into an album.
Zoom (manual on my lens) - autofocus - shoot short movie. Re-zoom.
Repeat
I also disabled the sound recording for now. That was really annoying.
Steve Thomas