Not sure whether you are responding to OP or me in No. 5 (or perhaps both of us) as we both mentioned 0 sulfate but I mentioned comparing near by wells and you discuss that. In neither case was testing by the municipality but in OP's case by a Lamotte kit. In my testing I use Hach Sulfaver (BaCl2 with excipients that help keep the precipitate in suspension). The test is described as being suitable from 2 - 70 ppm and its sensitivity is 0.4 ppm/0.010 Abs so at the lower limit we'd have A = 0.050. Thus, when my friend's well read A = 0.000 I was pretty confident that there wasn't much sulfate in it.
I did mention in No. 4 that the precision of the LaMotte kit is pretty rough so that OP might well not detect 5 - 10 ppm with that technology.
Also, and I'm relying on memory here, I measured 3 ppm (using Sulfaver) in the rainwater of rural Quebec ( a neighbor there, a real tree hugger, had installed a rainwater collection system and was concerned about acid rain - bird poop, no, but acid rain, yes). If I was smart I would have evaporated the volume down considerably to improve the sensitivity of the test but I really don't remember whether I did or not.