Alright, let's give this a shot. The temperature difference is noticeable after mixing. We use a machine called a speedmixer; with the sample size in question and it's lack of viscosity of this particular solution the difference might be about 10 degrees C. My guess is that the dark particles/droplets are NaOH with a tiny bit of indicator. Becuase of the solubility problems with NaOH in our solvent system, we are going to try another base that has been ordered. Perhaps it will show normal titration behavior and this is all just a strange pH depended solubility thing.
As for the question of water. This is one we have been considering as well. By weight, we add 50% NaOH in water. So we're not adding much, but in a solution lacking water the effect on the pH probe could be significant. Strangely, if it were reading the water phase (not obvious as a second phase in the solution, but seemingly well dispersed) one would intuitively think it would immediately start reading a very high pH upon addition.
None of the solvents are organic acids. One of them is, however, a protophile. The other two should not affect the pH by direct H+ release or uptake. Again, no real phase separation is noticeable, and the "particles" are solid as seen under a microscope.
I'll keep you updated with the progress when the new base arrives and we repeat the titration with a soluble base.
Here's another observation in the mean time: When you titrate the solution up and its pH drops down after a certain base addition or additional mixing, the phenomenon only happens once. Upon further titration, everything follows a logical progression with increasing pH at various rates until an appropriate endpoint is reached.