MAd King your approaches are within industry guidelines and allowed by building codes. It's just your approach is the bare minimum approach. I can not answer your question with a simple one liner since there are so many variables. If your going to piece meal a load of scrap board you are incorporating a lot more area to absorb water.
I would not go this route but rather the topical membrane approach.
I wish you well and hope your shower is a success. I will not personally say "Great" sounds like a winner since it is not how we build our showers. I would remind you that you have already saved the money a container of of Ardex 8+9 or a bucket of Hydro Ban costs. That money could make your bathroom's shower waterproof - not water resistant. If you want to follow the base grade standard this of course is your choice but if you go that route I would be using full sheets of backer board. So your back to the start.
Good Luck. JW