I just checked my water...
using my LCR meter, I get 7.7 ohms
then using my extech multi-meter I get about 15K, but like you, it changes, and on my case it is increasing, as I'm typing this, it is now 20K and climing.
now, I just swiched from Ohms to volts, and the cell had 240 milivolts, and dropping fast, now 222 mili.
so as I was measuring Ohms, the multimeter was charging the cell, and that is why the resistance using a multimeter changes.
now I checked the output signal on the LCR meter when in Resistance mode using the scope, and it has an AC wave. and that is why when using the LCR, it measures the acurate value 7.7ohms.
The Multimeter uses DC to measure resistance.