I guess you want cast because of fire code? Thats the only reason I'd use cast in residential.
In addition to Peter's reply.
That dishwasher and washing machine is considered an 's trap'. Those have been illegal pretty much everywhere for a long time.
That main waste line should be 3" due to the fixtures being drained into it, on top of the fact the washer requires one in a lot of places.
If you want some advice outside this forum, show that diagram to your local plumbing inspector or a plumber.
I know I'm basically repeating what Peter said, but it should be reinforced that the layout you have might have worked 50 years ago, but from what we know now, its not good enough to ensure a healthy piping system.