Why are you trying to mirror and not just draw in native apps? Not claiming you're wrong, just wondering what apps/workflow you're using, since "drawing" is pretty good on the iPad.
I probably wanna jump quickly between e.g editor / terminal / website and the whiteboard, and sharing the iPad monitor directly by joining the call seems to heavy.
I'll have to try it the way you describe sometime just to see how it works for me.
Yes, drawing on it in isolation is great, but it hasn't otherwise worked out like I hoped.