You can't just "tie the sink into the 3" stack". There is more to it than that, and offsetting the 3" above the floor would require the cabinet bottom to be about 10" above the concete. (You will also need some revisions in the ceiling to offset the pipe into the wall which will require the loss of some headroom.) Your present idea is flawed and will need some revisions. Have you also given consideration to the fact that the patio area probably does not have a foundation and footing around its perimeter, and if not, that area can "move' independently of the house itself?