I'm planning a claw foot standing tub at room's center.

It has 1.5" P-trap. The drain pipe it would connect to is 4".

Ideally this drain pipe would extend parallel along the floor joists to connect with the a 4" sink drain 13 feet south. Then the tub can wet vent via the sink drain.

But since the distance is too long, even though the pipe is 4" in diameter, code probably won't allow this.

Another option is to create a revent somewhere along this 13 feet drain pipe to the western wall. But holes must be drilled across four floor joists. This I would prefer to avoid.

The northern and eastern walls are exterior walls with windows, so best not to put vents or supply lines in them.

Tips appreciated on how to improvise the design.

Thanks