Screen recording of Keynote presentation (slides + annotation + audio)

I'm a university professor trying to find a way to record my keynote lectures (slides + annotations + my voice). Using Keynote remote on my iPad, I can control and annotate over Keynote running on my MacBook. Using iPad's screen recording feature I can record my slides, annotation, audio, but the screen recording is of presenter display. Since the presenter display on the iPad bounces from full screen to letterboxed screen with color picker when using the apple pencil, the recording is rather unprofessional looking.

Is there a way to force the iPad to not record the color picker + letter boxing? Meaning, is there a way to have the iPad screen recorder capture the viewer screen rather than the presenter screen?

The alternative solution is to screen record on my MacBook, but then I loose the audio input from the iPad which is some distance away.