This website illustrates a similar problem. They create a drain stub-out for the sink at a height determined by running 1/4" per foot from the waste stack. But they don't talk about how to make the sink connect at that height.. do you just add pipe after the trap to keep climbing as high as necessary before meeting with this stub out?
isn't 1 3/8" max diameter for a hole in a load bearing stud? here they're running 1 1/2" pipe through it? Is some kind of reinforcement used?