So, the work I was doing the other night was mostly implementing and testing the method described by Iwachido (Iwachido, Tadashi. "Modified titration of potassium." Talanta 13.12 (1966): 1697-1699).
The basic idea behind testing for potassium is this: As a general rule, all potassium salts are quite soluble in water, with very few exceptions. One quite notable exception is potassium tetraphenylborate (K-TPB). The classic test for potassium in seawater is to precipitate it by adding sodium tetraphenylborate (Na-TPB), and then carefully filter the K-TPB precipitate, dry it, and weight it (Sporek, K. F. "The gravimetric determination of potassium in sea water as the potassium tetraphenylboron salt." Analyst 81.966 (1956): 540-543).
Another, easier approach is to use a known excess amount of Na-TPB to cause the precipitation, and then titrate the remaining Na-TPB left over after all the K-TPB has formed (Schall, E. D. "Volumetric determination of potassium." Analytical Chemistry 29.7 (1957): 1044-1046). This method does require removing the precipitate from the solution before titrating, though, because the quaternary ammonium salt (QAS) used as the titrant will react with the K-TPB, giving a false high reading and a "chasing the endpoint" problem. This is the basic approach that the Red Sea kit takes.
In the paper I cited in the first paragraph, Iwachido addresses the problem of needing to filter the sample nicely by using polyvinylpyrrolidone (PVP), which deactivates the K-TPB, allowing the titration to be performed without having to filter the sample first. Iwachido also suggests using a lower pH for the titration by adding an acetic acid buffer (vinegar), which makes the color change easier to detect. I have found that I can get good, consistent results regardless of whether or not I use the acetic acid buffer, but the color change without the buffer is impossible to detect under certain lighting conditions (more about this below). While I've not yet had a chance to work with the Salifert kit, I'm pretty sure that it is based on Iwachido's method.
I made up the required reagents for Iwachido's method, but tweaked the concentrations a bit. I made the Na-TPB solution more concentrated (0.048 M instead of 0.02 M), and made the QAS solution weaker (0.0077 M instead of 0.01 M), so that they would match the concentrations of the corresponding Red Sea kit reagents. This lets me compare the results of the Red Sea kit and my own reagents side-by-side.
I will say that I have experienced the problem that many people describe, of the color change that never seems to happen, with the Red Sea kit. I also witnessed this same phenomenon using the Iwachido method, if I skipped the acetic acid buffer step. After some experimentation, I have found that the ability to detect the purple-to-blue color change very much depends upon the light source. Even away from my tank lights, under certain ostensibly "full spectrum" and "daylight" artificial light sources, the sample continues to look purplish, even when it is clearly blue or even blue-green under different lighting. I have also found that it is possible to adapt the Red Sea kit to get the more easily detectable color change by making the following changes: Simply replace 4 drops of Reagent "A" with 4 drops of RO/DI water, and then also, right before the final titration step, add 3-4 drops of distilled white vinegar. The indicator will turn yellowish or orange in color after the addition of the vinegar, and will be a distinctly different color after the color change. The exact color it will change to may range anywhere from bright blue-green to perhaps even a purplish color, depending on the ambient light source, but it will definitely be a radically different color than the starting yellow or orange. I find the Red Sea kit's dye to be a bit too intensely dark for my taste, and I find that I get more consistent results if I use the tiniest single drop I can get out of the bottle, instead of the suggested two full drops. This may have to do with the fact that the dye used, Bromophenol Blue, is a dichromatic substance (google it), meaning that its color hue actually depends on the concentration in solution and/or how much of the solution you are looking through.
I have also found that the tedious filtration step can absolutely be skipped if the PVP solution is added at the end of the 10 minutes wait time. Now, since you are back-titrating the full amount of solution, and not only 3 mL of the filtered stuff, then that means that you will need right about twice as much titrant to reach the endpoint, and that also means that each 0.01 mL of titrant roughly equals a 1.5 PPM change instead of a 3.0 PPM change in the potassium reading.
I'm having too much fun with this stuff.