I guess I'm confused. In the first test, if you multiply the calcium ion concentration from the external lab (770) by the conversion factor for Ca-to-CaCO3 conversion (2.497), you get a number very close to what you measured using the Taylor kit (1960ppm versus 1922ppm).
You then you tried to "soften the water" (what did you do to "soften" it??) and now your numbers don't match....so what did you do?
The Taylor test for calcium absolutely removes magnesium. First of all, the R-0010 calcium buffer causes free magnesium to for magnesium hydroxide which is a solid precipitate. Also, the R-0010 raises the pH up above 12. In doing that, the indicator dye reacts more strongly with calcium ions than any other divalent metal. The R-0012 titrant then removes the calcium from the dye complex and that causes the indicator color to change. The only other interferences in this process can come from other divalent transition metals, most notable iron or copper. HOWEVER, the R-0012 is formulated with at least two chelating agents - one for calcium and one to strongly bind up other metals. So the test most definitely does not measure total hardness. As I said previously, if your Mg levels are very high then you might need to add more R-0010.
Here's the issue I think you might be running into - fading endpoint. When the CH level is very high (above 1000ppm), you have to use A LOT of drops of the R-0012 and, in fact, you likely should add an extra drop or two of the indicator dye. The problem I have noticed with very high CH is that, as you get close to the endpoint, the color transition from the intermediate purple shade to the final end point of blue can fade back and forth very quickly. So, you can actually add too many drops of R-0012 because it will transition from purple to blue and then back to purple very quickly. There are two ways to get around this -
1. Add the R-0010 and then, before adding any indicator dye, add half the number of drops you'll think you need of the R-0012. By doing this, you'll lock up some of the calcium ions BEFORE the dye can bind to them and it makes the transition point more crisp. You must count ALL of the R-0012 drops you add as your total amount of titrant - the ones before the dye and after.
2. Dilute your sample water 1:1 with distilled water. While this will technically make the accuracy of the test lower, it will cut the amount of calcium in solution by half. Doing this, along with step 1 above, can make the end point much more crisp. You will sacrifice some accuracy in the process.
Also, you should always report hardness (calcium or magnesium) in units of calcium carbonate concentration (ppm of [CaCO3]). It's how most of the titrants are calibrated against AND, when calculating saturation indices, the formulae for that always expect calcium hardness and TA in those units. I realize the ICP-MS lab reports will show them in ion units but that's because of the way they measure the ions in solution and how the equipment analyzes them. For aqueous water chemistry, everything should be converted to CaCO3 units.
