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the plumber is now getting sloppy, and says it has nothing to do with his workmanship. Last year, when he installed the new bathroom, the smell was much worse, and he had forgotten to put silicone around base of the toilet. He did this, and the smell slightly improved for a while
This points to a wax seal on the toilet that has ruptured allowing sewer gas to escape into your bath room. I don't think adding another vent will help a bit. Sounds like your plumber was stumped and just threw that out in hopes it would help. I would pull the toilet and reset it using a new wax ring.
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The plumber says that if all 3 bathroom pieces have their U bends,("P" traps) - itīs not possible for smells to pass through the water - This I know is not the case, as gases are heavier than water
You are in error about that. This is why we have traps on all fixtures. The water acts as a seal against sewer gas. But I would take care of the lake of stagnant water under your house and replace the wax seal. Good luck, Tom