If you raise the floor in the bathrrom you will now have a step to consider when entering the room, I moved our bathroom location from one side of the house to the other, but I took the waste out through the wall and linked up with main sewer.
I think you should get at least some information from the council as to the requirements for run and fall.
I have noticed that many of your answers have come from people in the US The USA is completely different to our building codes and you should take that into consideration.
Here we have a one quarter inch fall per linear foot , and they have all kinds of things that would never pass a building inspection back in England.
My guess is, that if you live in a purpose built block of flats, the floors are solid concrete, that on it's own would be a challenge. If you do have floor joists, I do not think you would have sufficient space under them to get the desired fall over a 13 foot run. A project like this one is very difficult to judge without actually seeing the lay out of the property, and being able to determine the best route to take.
Just to give you an example of the difference between here and England, they still run a single wire from socket to socket and have never heard of a ring main. LOL When you plug in a vacuum the lights flicker, I am not lying, but all this is acceptable by local code and building permits.
Although I love living and working in the US, it's like stepping back in time within the building industry.
Good luck with the project.
Paul M