George,
I don't recommend charging over night especially the 8.4V version. You can do a quick charge while attended, otherwise remove battery and charge with a plug in unit, or use the MTH charger if it has a charge port.
My first choice would be to use an MTH charger, however, from the tone and content of the OP's posts, I seriously doubt that he has one.
Regardless, I must disagree with your preferred choice of externally charging the battery.
My experience, after literally hundreds of times charging unattended both 3 and 5 volt PS2 engines without any issues whatsoever, is that any risk of an "anomaly" while charging overnight is much smaller than the risk of inadvertent damage by a relative novice opening up a PS2 engine, extracting the battery from whatever inconvenient place it's been stuffed, reinserting the battery, and closing up the engine.