Island Vent Loop Question

[Pauly79]

I'm in a two story condo, and am relocating the kitchen island.

The kitchen is on the second level, and the the current set-up involves an underfloor p-trap connected to a 2" drain that connects to a vented drain in the service wall.

I wanted to remove the p-trap from under the floor because it causes the bulkhead its in to be an extra few inches deep and as the bulkhead will be expanding horizontally as part of my renovations, its depth will cause problems with the opening of the front door. Removing the p-trap and putting it above the slab will allow the bulkhead to be expanded without interfering with the door.

My plumber is suggesting the use of an air admittance valve, which can be placed above the rim of the sink inside the island since the back of the island has a 6" deep ledge that rises 6" above the normal counter height.

However, I've been reading about island vent loops and am wondering if one might work in my case. Basically, I could run a loop vent like in the attached image, except the vertical vent part of the loop would connect directly to the horizontal drain, and then that drain would be connected to a stack at the service wall, since it would be very difficult to create a new horizontal vent that connects to the stack.

Is this possible solution, or do you need to have two separate horizontal vent and drain pipes running parallel to each other?