I'm sorry but that set up won't fly either. All codes mandate that you can not discharge a major fixture, such as a toilet past a unvented minor one, (such as your vanities). You have three options,
1. Run a vent out the roof or revent back to a existing dry roof vent in the attic.
2. Revent into a fixtures dry vent at least 6" above the flood rim of that fixtures. **OR**
3. Install a AAV,( air admittance vent) but out where it can be serviced and not behind a wall.
Either way you're going to hafta go up instead of down. Good luck, Tom
