Chlorine at pool/spa pH (i.e. in the 7-8 range) does not outgas as molecular chlorine (Cl2), but rather as hypochlorous acid (HOCl). The Henry's Law constant for Cl2 is 0.093 M/atm while for HOCl it is 660 M/atm so chlorine gas is 7000 times more volatile (from an equilibrium perspective). However, in pool water with an FC/CYA ratio of around 10% and pH near 7.5 and 350 ppm chloride, the HOCl concentration is over 3 million times higher than Cl2. At these concentrations, the equilibrium pressure of HOCl is roughly 500 times higher than Cl2. It is HOCl that outgasses at pool/spa pH, not Cl2. (A saltwater chlorine generator pool will have the Cl2 outgas 8.5 times faster than my example, but that's still over 50 times slower than HOCl).

Now that said, the aeration to remove chlorine from tap water is with chlorine that has no CYA in it so is roughly 10 or more times higher in concentration and it usually takes quite some time to lower the chlorine level. Even so, it's a possibility and one that could readily be tested on its own by using just using the Speedstir on its own before doing the test and doing so for different lengths of time. If the measured chlorine level declines as a function of the stirring time, then the loss from outgassing during stirring may our culprit.