What is the right way to plumb bathroom drainage across small joists?

Finished the demo part of the bathroom remodel to find pretty significant damage to the floor joists caused by the original builder’s "design" (see photos/video). Setting aside how I’m going to fix or at least mitigate the damage – what would have been the correct way to plumb in the toilet and sink drains without weakening the structure?

Given the small floor joists, I can’t imagine the right way to try to drain across them this way. So what would a pro builder have done to install this bathroom correctly?

More photos

More context:
This is the 2nd floor of a 2-story, 1920s house. This bathroom and its stack are directly above the 1st-story bathroom. The stack is perfectly vertical from the basement to the attic, where it has a slight offset to exit the roof. The existing stack is cast iron and all existing drains are steel/iron.

The toilet drain pipe in the wall drains both upper and lower commodes before Y-ing into the main stack 5′ above the basement floor.