Well, we finally got this problem resolved! Sorry it took me seven months (!) to update this thread with the solution. I had completely forgotten about it all summer. Apologies for the long post, but we went through an awful lot to get this resolved!
Last time I posted in here, the warranty guy from the builder was coming over to remove the baseboard in our laundry room and check under the shower pan for leaks. Well, that produced no results. It was completely dry under the pan. A few weeks after that, we called a completely different plumber here in town, explained the situation to them, and had them come over. They performed their own smoke test, but did it differently than the builder's contracted plumber. The one we hired took some pool noodles wrapped in towels and used them to plug our main drain pipe via the clean out lid out by the street near the front of our lot. That clean out is about 70+ feet from the cleanout they put the smoke into. That one's right in front of the house, hidden under some hedges. The result was a crazy amount of smoke coming out our two roof vents, something we never noticed when the builder's plumber did their two smoke tests during previous visits. This was likely because they never plugged the main pipe at the clean out by the street!
One of our roof vents exits out into a totally open section of shingles with nothing above it or around it. However, the other vent was located very close to a wall, and 2 feet underneath a soffit vent (see attached photo.) When the plumber we hired went into the attic with a flashlight and looked around, he located smoke that was coming in via the soffit vent. However, since no smoke came in through any shower, toilet or sink in the house, the plumber suggested that our shower drain was smelling due to insufficient ventilation to the outside air. He said that with five drains in our master bathroom (shower, corner tub, two sinks, and a toilet), the single vertical vent was not capable of handling all that, and they would possibly need to add a second vent in our master bathroom that lead up to the roof. Now, our foundation is poured concrete slab, not a crawl space. The plumber's loose estimate for digging into our foundation and adding the additional drain was anywhere from two to five thousand dollars. To his credit, he did suggest we ask the builder to move the vent located under the overhang first to see if that would fix the issue, since that was the cheapest solution. Plus the fact that the vent never should have been in that location to begin with.
Now that we had gotten another plumber's opinion and another smoke test (at a cost of $485), we took this information to the builder. They shared all this with the original plumber, and together agreed that another visit to our house was necessary. So right around the start of summer, we had the owner of the original plumbing company, as well as the chief construction guy from the builder (can't remember his exact title) come over at the same time. Both of them agreed that the roof vent was poorly located and never should have been installed there in the first place. The plumber agreed to move the vent further up the roof, and the builder would have the roofing company come seal the old vent hole and install the lead boot over the new vent, all free of charge. Remember that our original bumper-to-bumper warranty on the house had expired at the end of February. However, since there was a long-standing record of us complaining about the smell for many months, they agreed to fix everything at no cost to us. Also, the owner of the plumbing company voluntarily offered to fully reimburse us the $485 we had paid to have a smoke test and assessment done by the other company.
Next, I discussed with them the other plumbing company's plan to dig into our foundation in order to add another vent. The plumbing owner told me that our roof vent pipe was definitely large enough to handle one half of our house. He said it's possible the lead boot could have been poorly folded over the top of the PVC when it was originally done, thus blocking some of the air flow. Since the the pipe was getting moved further up the roof anyway though, the builder's construction guy said he would make sure the roofing company did a clean job when they came to install the new lead boot.
Finally, the builder's guy asked me what water heater we had. I told him it's a State brand hybrid electric heat pump (
link). He asked me if I had flushed it yet since we moved in and I told him no. He said that there had been a few other homeowners in houses built by their company that were having issues of smelly water coming from this particular brand/type of water heater. So, he and the plumbing company owner said that in addition to relocating the roof vent, they were going to drain our water heater and do a complete chlorine flush of our entire plumbing system.
A few weeks later, we had a new roof vent, a clean water heater, a completely flushed plumbing system, and
NO MORE SMELL! After many months of a smelly shower and bathroom sinks, plus endless frustration, we finally were able to put this issue to rest and enjoy our home again.
The last bit of advice the two of them left me with was to completely drain our water heater once a year (after turning off its circuit breaker), and to pour a little splash of bleach in our master bathroom sinks and shower drain, then let it sit overnight before flushing in the morning. They recommended we do that every four to six months.
Whew, what a mission. But we're finally free!