Other options for an air admittance valve besides underneath the sink?

I am re-doing the plumbing in my 1950's house and the ventilation is really poor. I have replaced the entire cast iron stack from the basement sewer up until the beginning of my second floor with PVC. Two bathrooms are on top of each other, however, my downstairs toilet gets tons of air bubbles and empties the bowl when the upstairs toilet is flushed. I have not tackled the plumbing for the 2nd story fixtures, yet, but I will. They are a nightmare of Y's and T's embedded in concrete mud bath and even with the 1st story bathroom's ceiling open up, I can't see where the pipes run and connect to my vent stack in the attic. I am fairly certain there they are clogged. For now, I am hoping to put a air admittance valve somewhere for the first story fixtures to help with ventilation for now. I am trying to put it in a place easily accessible in case I need to replace it.

Below is a underneath view of how the plumbing is set up on the first floor:

Basement Plumbing

That bathroom sink line is where I am contemplating putting a AAV. Below is a dry-fit of what I am thinking after it comes out of the wall...

Underneath sink

I see that this is a common placement for AAV's, but, it doesn't allow for very much room to hook my P-trap up to my sink drain. I'm wondering if I can put this AAV somewhere else underneath my first floor and if that will be effective. For example, could I put it somewhere between the bathroom sink drain line and my main stack... does it matter where it goes? So long as it is above where the water flows high enough, is that enough?

Could I put it like the picture down below? I could put a T there and have it running up and above that section?

enter image description here


Thanks for your help, HI!