The way you are expalining it now might work. Looks very reasonable to me if you keep volume changes.
I've been thinking there might be a correlation between the liquid specific gravity and its conductivity... After all, changes in the liquid density are related to changes in its contents; that is its chemical composition. Even if the relationship is not linear the mathematical equation can be obtained (not hard to do I've done it several times) and linearize the thing in the soft to extrapolate the specific gravity from the measured conductivity. You can to research that. Probably someone tried that already. If you can't find nothing some experimentation may yield some measurement values we can work with. Conductivity measurements are way easier to perform and it can be monitored continuosly. I have doubts about the cleanliness of the eletrodes ,etc to be suitable for your particular case though. 