Sounds like you have identified the likely sources of the bromine, and I'd be leaning toward mislabeling/packaging, too, but I was wondering... is it possible that your test strips got contaminated (I think the bottles usually warn against reaching in), or that the bromine section is picking up a free or total chlorine reading? If I remember correctly, my strips have a section for Total Chlorine, and one that reads Free Chlorine or Bromine, but no section for bromine alone. I think my Taylor kit uses the same reagents for chlorine or bromine, so I don't know how a test strip would differentiate.
I also was wondering if your alkalinity problems could be affecting your readings (chlorine changes forms at high pH). Are your alk and pH levels balanced now?
Just curious, if there is bromine in there why do you need to get it all out of the spa? I am pretty sure you can shock a bromine tub with dichlor, so I don't see why they can't co-exist -- unless you have some allergies.