1.2V AAA rechargeable batteries, voltage for almost full charged cell
It sounds like you completely discharged them, then charged them at 350 mA for less than 2 hours. I doubt you over-charged them. To be sure, you can measure the capacity after you fully charge them. If the capacity is similar to original (or similar to rated) then they are probably OK.
With NiMH batteries, charging does not rely on voltage thresholds for end of charge. The charging is terminated using either dV/dt or DT/dt criteria. In other words, the slope of the voltage change is observed during charge at constant current, or the slope of the temperature change is observed during charging at constant current. The charge rate should be at least C/3 in order to generate a strong dV/dt signal. C/2 is better.
I will let you search the details yourself as you seem to be quite resourceful and are proceeding on the right track.
In order to accommodate both AA and AAA, you will need to select different charge rates. AAA will want to be charged at 350 or 500mA. AA should be charged at the highest practical rate. At least 700mA. If you cannot do this automatically, then the user should do it with a switch or something.