Edit: read yours again my answer below isn’t helpful at all! not picking up till the bottom of the stroke sounds like it would definitely hinder learning moving off, means barely any forward motion from first pedal, needing to get the other foot up and pedaling straight away, with not much momentum to help balance. Good luck!
Previous non answer: not really an answer, but I hired a bike in Copenhagen with a coaster brake and I hated it. Well, got mildly annoyed by it. setting the pedals just before coming to a stop at traffic lights – sudden jolt to a stop – usually alarming wife just behind.
Back pedaling to set left foot forward to keep front up while popping off a kerb – hilarious consequences.
Basically a few habits that were totally unconscious from years of riding bikes, that kept tripping me up. I can imagine it wouldn’t be as bad if you were learning with one from scratch, but I can imagine having a coaster brake being off-putting.