I'm not an expert in this field but I'll put my 2 pence in.
Firstly I wouldnt use gas welding rods, esp 308, there is still ferritic metal in 308 its a fairly low grade, and there might be other compounds, fluxes anti oxidisers etc, you'd be better getting a couple of stainless electrodes for a liquid level device as spare parts.
You probably allready know that you'd need ac on the probes, using 2 outputs of the pic and aletrnating between 01 and 10 for the samples, to avoid electrolytic action from eating the probes.
As I remember water has a non linear curve between 2 millsiemens and 4 millisiemens, I know that from testing chiller water for inhibitor treatment on cooling towers.
I think the best way round the linearity issue is to make up some known solutions and take readings, then code the system to interpolate.