You have a lot going on trying to cycle a tank at the same time you are treating with copper. I'm not saying its impossible to do, you just have a lot of variables to manage.
Bacteria in a Bottle products all take more time to cycle a tank than what's needed in an emergency. It's possible the sponge you have from the display tank sump had not adequately collected enough of the nitrifying bacteria to work. If the display tank was not fully cycled when you transferred the media to the QT HOB filter, it would not have carried enough bacteria with it.
Usually, when a tank has cycled the ammonia drops to 0 and nitrates rise. In a QT tank with nothing to export the nitrates, (ammonia>0) + 0 nitrates = not cycled
I suspect if you used both the salifert and the red sea at the same time you would get fairly similar readings, assuming neither kit is out of date.I tend to be suspicious of the Seachem Dot, don't know how to tell if its out of date. But, there are reasons it may show a different reading than other test kits.
Info Below from another website: ( https://aquariumscience.org/index.php/5-2-safe-ammonia-levels/ )
The toxicity levels of ammonia are shown by the Seachem test kit which measures the free ammonia levels rather then the total ammonia levels of the API test kit (and others):
This Seachem test is for free ammonia gas, not total ammonia. The API test kit measures total ammonia nitrogen (TAN), not free ammonia gas.
The most accurate way to illustrate the toxicity of ammonia is a chart derived from the University of Florida ammonia toxicity chart (Publication
#FA16, “Ammonia in Aquatic Systems”, Ruth Francis-Floyd). This chart translates the Seachem dot test of ammonia gas to the API test of total ammonia as to toxicity levels:
The API test measures BOTH the ammonia gas and the ammonium ion. This is called “total ammonia nitrogen” or TAN. So one needs to look at the pH of the water when trying to determine the toxicity of ammonia as measured by the API test. The toxicity of total ammonia is ten times greater at a pH of 8.0 than it is at a pH of 7.0. . Over and over one will hear “
ammonia kills at anything over 1 ppm“. This isn’t true IF one is talking about the API ammonia test results, or any other test kit that measures TAN.