Maybe the stirring is causing the chlorine to outgas. Yes, your suggestion of trying turning off/on Speedstir between drops to better simulate the amount of manual swirling would be a good test. If having the Speedstir not swirl as much is making a difference, then swirling is the culprit, though I would have the expected that if you took longer with the Speedstir (so longer time swirling) you'd have an even lower result than you've been seeing.

If swirling was causing more outgassing, I'd expect the pH to rise so one other test you can try (you already tried TA and found them to be the same) is the pH test. See if the longer you swirl the higher the measured pH using the Speedstir.