what about the floor drain next to furnace? shine a light in the top and see if you see water, if the trap is cracked or dry its possible its sucking sewer gas into a loose return at furnace and through the supply vents. (also if you have a sewage ejector pit for basement plumbing, make sure the lid is sealed as it will do the same thing.
It is a definite possibility that your water heater is spilling flue gas at start up, and then vents properly after it has run for a while. The cause of this could be that your openings to your return ducts are depressurizing the basement. When the flue gas spills from the water heat flu pipe it is sucked into your air handler via the return side and then distributed to your supply vents.
Get someone out their to do some pressure testing of your basement and testing of the water heater venting.
The reason why this does not happen in winter can be due to the fact that it is colder outside, so your water heater flue gas vents quicker/easier. Also, your furnace runs in winter and that assist the venting process for the water heaters.
Had the venting scoped. Flue vents, ac vent, wall cavity all look clear. Also smell clean. The smelly air must be getting drawn into the air handlers and not from the ducts themselves.
Since the problem only occurs related to the master shower hot water I think we will focus our attention on the drain line.
AJ wrote, "The smell is present in all vents serviced by this AC unit."
Now AJ writes "...the problem only occurs related to the master shower hot water".
All I can take from this is that the smell is being distributed through all of the supply vents connected to the air handler in common with these vents. Not sure how you are connecting the smell with the master shower hot water.
if the sewer gas not from flue, but from plumbing is getting sucked into the air handler/furnace and the nearest supply is close upstairs to this, plus if this is the bathroom you use mostly for showers you spend enough time in there to notice it. (just a thought)
again look at the sewage pit, not the sump pit, and verify the lid is sealed, and the cord ports (usually we put the pit in the mech room next to furnace)
The smell is triggered by the operation of the master hot shower. It also seems to only happen once. We reproduced it yesterday for the ductwork camera contractor but then about an hour later ran the shower hot water and no smell.
Today i will try running hot water in the tub, but according to the previous owners, this will not cause the smell.
So something causes a sewer smell when hot water is run. Bacteria in the pipes? Something on the pipes reacting to the heat then burning off until it rebuilds or recollects?
If it is anything related to the supply side of the hot water that will be replaced when we replace the polybutylene (another problem not disclosed until we did the inspection).
Anything else to do diagnostically? I'm told you can't really scope an interior drain line. Might be something outside the drain line anyway reacting then the drain pipes heat up.
I put my nose right above the drain where the ac drain lines go and didn't smell the sewer smell. Is this what you are referring to?
Also for reference of other people researching this topic, other possible causes we explored was that perhaps a P-trap had dried out from less used plumbing fixtures in the basement. Or that the cleanout plug in the main floor drain in the utility room was allowing sewer gas to escape and get pulled in to the AC.
If we can't determine the source of the smell or the cause our next test will be a smoke test of the drain line service the master shower and bath. The leading theory now is that there is a crack in the ABS drain pipe somewhere that is expanding enough when hot water runs through it that sewer gas escapes and is pulled in by the return air handlers. Since we are not seeing any signs of water leakage and the problem has persisted for over 6 years, the crack is probably on the top of a mostly horizontal section of drain pipe leaving the master bathroom.