Rather than constant voltage, constant current is what produces the highest quality EIS.
The resistor prevents current runaway when the solution becomes more conductive, but with batteries the voltage is changing as the current increases. The battery set up with a resistor works very well, but a constant current system with an automatic shut off does it slightly better.
If you start with pure distilled water, you should end up with a very clear silver solution that has a good Tyndal effect. This is about as good as ionic silver gets.