Attached is an image with constraints labeled. I'm having a hard time figuring out how to connect all this together. My best thinking so far is to run the shower with a center drain to the toilet with 2". Run the toilet out the double LVL (engineer says OK) with a 3" basically perpendicular to the West Wall into the attic space. Vent it with a new vent out the roof immediately upon exiting the double LVL (this is very close to about 5'4" from the P trap on the shower which I think is max distance... although maybe the conversion from 2" to 3" at the toilet gives me a few more inches of space to work with?). Then turn it with a long sweep 90 horizontally to go down the North side wall near the West wall of the laundry on floor 2 down to tie it into the main waste line under floor 2.
As for the vanity run a 2" waste pipe through the South wall into the attic space on the west and bring it back around and tie it into the 3" I sent down the laundry wall. I'd probably vent this immediately out of the south wall through the roof, or if code allows maybe just do an air admittance valve for the sink.
Any suggestions? How would you plumb this with all these constraints?