This is just 1 of those things that look good on paper. If it was this easy, it would have been done long before you thought of it.

Bottom line this for even a simpleton. You cannot plumb like this. Code withstanding. You will have drainage problems.

The fact you do not understand why this will not is the difference between you and me. I know it will not work, you on the other hand, are asking a question and refusing the answer.