(i'm not a plumber) One thing I would do is put more venting in the design at the start -- easy when it is still only on paper. Otherwise I cannot comment. I would have a vent come down to connect
1.) between tub and toilet
2.) between toilet and shower
3.) and a 1.5" at the lav that the lav P trap connects to
You seem to know your stuff; you covered everything in very few words.