This question is a follow-up to my earlier one about a sewer gas issue in my house.
Since posting, and with the help of some of the comments, I've isolated what I believe is the problem: When the first floor bathroom toilet is flushed, it siphons water out of the shower p-trap. I have confirmed that when I notice the sewer gas smell, pouring some water down the shower drain makes it go away. Then, if I flush the toilet in the same bathroom, it comes back.
Because this portion of the drain system is not vented and instead uses an air admittance valve (AAV), I'm concerned that there may be an issue with the AAV. Is it broken? Too small? Are the drain lines not properly installed?
Here's what the plumbing looks like from below:
Here's the AAV:

