[Arkcon]

Hydrometers, at these level won't work well enough no.  And I wouldn't want to be using a pychnometer for the same assay, even if it might work.  A conductivity meter might keep you in the ball park, however.

You are utterly obsessed with your water conditioning PVC shell tablet.  Now I've heard of people putting slow dissolving tablets in home aquariums, to buffer the water and remove toxic compounds, but I've never heard of that on a larger scale, for a permanent duration.

I've heard of small pools being chlorinated with a slow dissolving tablet, for a short time.  But I've never heard of an Olympic sized pool being treated with a giant tablet.  And again, that's asking for only one additive, not several like you need.

I don't know how many examples of how infeasible your plan is you really need to hear.  Or what counterpoint there is.

[Enthalpy]

The conductivity would give a very rough measure of how pure your water is. It won't tell the detailed composition. But it will tell if you have already added the salts, for instance.

The apparatus isn't completely obvious to build, but it can be purchased. Short training before use.

[DrCMS]

The only way i can see this might work is to have a header tank with a concentrated solution of salt to give ions in the correct ratio that is dosed into the water trough whenever fresh water is added to the trough.  It would be quite a bit of work to get right.

[Enthalpy]

Or have a set of big tanks to feed the cows. A human operator opens a tank's vane that fills it with water and adds the predetermined amount of salt (preferably as brine), closes the filling vane, waits or stirs, and opens the vane that waters the cows from that tank. Rotate the tanks.

But if the process shall be automated, then a conductivity meter can inform the servo loop that determines how much brine must be added to the flowing water. If the flow changes only slowly, it must be feasible.

[GentryMillMan]

Aren't there mixing valve/manifolds that currently allow for a measured concentrate (powder or brine) to be mixed with an incoming liquid?

Minimum flow rate of current filling valve vs the maximum flow rate of same valve and what concentrations would need to be to maintain target final solution?

I can't help but believe there is no way to keep an accurate solution by throwing a big concentrate pill in the tank.  There just seems like too many variables on how much the cows drink on a day to day basis.