I don't know what would be considered a K overdose or what it might do. I think KNO3 is generally considered safer than the nitrate formed by the tank's biofilter. But again, I'm not sure, I make sure to keep N at ~10ppm at all times. I'm sure anything can become toxic at elevated levels.
In regards to the API reagent, the API reps suggest you bang bottle #2 on the table as well as shake it for a minute (rather than the 30 secs the directions advise) . They claim this will avoid false negatives, not sure why it's not written into the directions. Also not sure if it'll affect your readings, but it's worth a shot. If I'm noticing things correctly, you'll see little silvery dots in the drops of N reagent bottle #2 when it's mixed correctly.
Have you tried testing distilled or RO water to rule out false positives? Left C has a calibration technique written up here, somewhere. By using that, I've found my API N reagents to be pretty accurate, maybe a tad off in color by about one ppm (my measurements of K were not done any more exact than a tenth of a gram, so lack of control could have skewed my results), but certainly closer than any of the other cheap reagents I've tested, like the Hagen.