Seems to me you just need to have a 3” running from the vent back to the shower and sink, then use your wye’s to dump into it. Put a vent on the sink and tub, the toilet should be able to connect using a wye, into the main 3” run if you have the room. Then your shower seems close enough that the vent on the vertical stack should work.
But I’m not a plumber!
But I’m not a plumber!