Yes, the house has a radon system, plus a radon test just last year showed levels on the very low end of the acceptable range. And even if it was high, radon (to my knowledge) also does not cause headaches, dizziness, nausea, blurred / double vision, rapid heart rates, etc. Also, re: the sump pit, no, the lid is not sealed. If it was sealed, I would not be able to stick the probe of the gas detector into the U-shaped hole in the lid, nor hold the probe above the hole, to take measurements.
Still trying to get someone out here to inspect the extractor pit. The local guy we're working with now is not known for his punctuality.
Back in 2016, the check valve on the extractor pit failed and it took a while before anyone noticed. I'm wondering if the water rushing down the extraction tube and back into the basin may have somehow damaged a seal.... or if there's been a fume leak going on for sometime... that is leaking below the concrete in getting into the inlet to the sump pit which is only 12-14 inches away. That's the only thing I can think of as a cause for what's going on.