Please help with new basement bathroom DWV piping layout.

[chachee]

Quick background details, House was built in 1952 with unfinished basement, concrete all the way up to the first floor sills.

The main floor bathroom has a 4” cast iron stack that leads out the front of the house, away from the proposed bathroom location and is approximately 20” below finished slab elevation (located by local plumber).

Kitchen sink at the back of the house has a 2” pipe with 1- ½” vent drains the kitchen sink (main floor), floor drain, utility sink and clothes washer (basement) and leads out of the back of the house approximately 10” below finished slab grade and is near the location of the proposed bathroom.

Having trouble laying out the waste piping and provide the required venting, either through the roof or AAV.
Total DFU if I connect to the kitchen pluming = 13 which leads me to 3” piping from the water closet with 2” vent(?). Please offer up suggestions on how to plumb the bathroom drains.

Increasing 1.5" vent for kitchen is not feasible as it would require going into wall cavity behind kitchen cabinets with granite counters. Let me know if there are any additional details I need to provide.

[chachee]

Haven't received any feedback so here is my first attempt at a layout.

Concerns/questions
1. Can an AAV be placed in a wall cavity? where do these usually go?
2. Is there sufficient venting for the shower between the 1-1/2" and 2" AAV?
3. Can the drain and vent for the clothes washer go around the corner in the wall framing?
4. Can I use a Fernco coupling to connect to concrete?
5. I assume I have to use Ductile Iron under the footing?
Any feed back would be greatly appreciated.