Oh, that sounds really frustrating and concerning. I'm not an expert in the matter of Indoor Air Quality, but it's weird that the issue has stuck around for so long. Maybe check if the basement is well-ventilated? Sometimes, that can make a difference.

Also, consider other things that might be causing allergies, like mold or dust. The type of material in the carpet could be a factor too. It might be worth getting some professional testing for the air quality in the basement to see if there's anything specific causing the reactions.

And if the installer and manufacturer are brushing it off, maybe get a second opinion from another carpet expert or even an allergist. Keeping a record of everything that's happening could also be useful in case you need to take it further. Health comes first, so maybe consult with a professional on this one.