I think api possibly reads better than the Salifert tester. I have the Hanna TAN tester, the Salifert, API, and RS, and a few others. Where they lack reading is below .25 but with copper when it’s new QT tank, or when a WC was done, you will get the .5 false positive all the times it’s about 48-72 hours after a fresh dose of copper that you will get better readings of TAN. The badges for me have been hit or miss. I stopped using them. The amount of ammonia needed to kill fish would surprise you. Randy, our local chemist here, has a whole study written up about it. Sure is interesting. I will try to source the article and post it here.
And through all of this, I forgot to ask, and missed it in the other posts. Have you been checking on the fishes gills? Are they looking normal pink? I would assume no with the breathing being elevated, but I’ll leave it to you to post the info?