At this point running a vent under the floor is highly impractical since I'm on a concrete slab.
You didn't mention the concrete slab floor in your original post. In this case, an AAV is probably your best solution.
Can I ask why the AAV is not recommended? I've actually been using my sink without the AAV, just like the picture and the only sounds I hear are when I dumped a big pot of water there was a little gurgling. I haven't had any strange smells.
1. An AAV is a mechanical device. Mechanical devices require maintenance and are subject to failure. A true vent is simply a pipe open to the atmosphere and is essentially maintenance-free.
2. If an AAV fails, it can allow the release of unpleasant and flammable/toxic gases (e.g., methane, hydrogen sulfide) into your living space. A true vent releases these gases outside the building envelope.
3. An AAV typically has a poppet valve or a rubber diaphragm to allow the one-way admittance of air into the drain pipe. As the water travels down the pipes, it creates a suction in the piping above the draining water. This suction causes the AAV valve to open to allow air into the pipe so the P-trap is not sucked dry. As the poppet or diaphragm opens, it quickly relieves the suction and the valve may close again. Then the suction builds and the valve opens and closes again. This can happen very rapidly and may create a sucking/vibrating sound like cow flatulence. Not exactly something you want guests to hear in the middle of your dinner party.
Regarding point #3, there are a lot of AAVs on the market and designs change. Hopefully, they have improved to the point where this sound is uncommon. But I have heard AAVs make this sound before.
As for leaving that vent pipe open, I would strongly recommend
against doing that, even temporarily, if you are living in the house.