Hi mate, this all sounds very solid.
You sound like you have put a lot of thought in the program, lots of people get caught up with a 3 day bench program of 3 days of just benching
Back and core day works in fine. Maybe on that day rotator work and stretching could be introduced.
I would suggest keeping the 3rd day in and only drop the volume if need be.
Light bench 5-7 days out
Hope this helps, keep me posted.