wwhitney
In the Trades
Before you go very far down that route you need to take some careful measurements. If you have a laser level, easiest way to check would be:I think my best option is the separate sink drains you proposed.
Set up the laser level for an arbitrary reference elevation. Put the solvent weld trap where it wants to be, with the bottom of the u-bend on top of the drywall, and measure the elevation of the trap outlet (center line). Go to the first joist that the new sink drain would have to go through and measure the top of the joist. Subtract 2" for the maximum allowable top of hole, and 1/2 the pipe diameter for a 1.5" Schedule 40 pipe (which comes out to 0.95"). The difference of your trap outlet center elevation from this center of pipe in first joist hole elevation, plus 2" (the shower trap arm diameter, which is the maximum allowable shower trap arm fall), is the available fall for the sink drain.
Now measure the length of the exact path the sink drain would have to go to get from the hole in the first joist to the wye where the shower trap arm would join it. Divide the available fall by this length to get the maximum possible slope. If it's at least 1/4" per foot, the idea works. If it's less than 1/4" per foot, it doesn't work. [If you only need 1/4" or less of extra fall, they make a low profile 2" p-trap.]
Adding on there is not insurmountable, you would need access from above to that pair of elbows forming the vent offset. But the elevation of the new san-tee that you could add there might still be too high, would take some checking.I kept my drawing simple, but the the vent coming of the stack is already a bunch of elbows(see pic below), no way I'm adding anything there.
Or if you can open up the wall below, you can leave that vent offset as is and add a wye to the stack in the wall below, near the top of the wall, to receive the shower drain. Then the shower vent can join the yellow vent line higher up, above the vent offset.
Cheers, Wayne