[GTP Dad]

The reason you could not put water into the engine without it spitting back was because the engine temp was greater than the boiling point of water. The loss of coolant is probably coming from the heater core especially since you are seeing such a great a loss of coolant in such a short time. What you need to do is to pressure test the system so that you can find where the water is coming from. Pressure testers should be available for loan at Autozone. Fill the system and then pump it up to radiator cap pressure you should then be able to see any leaks and track down where the water is leaking from.

Also removing the thermostat is not a good idea and can actually make overheating worse. Once you find the leak and repair that replace the thermostat.

I would also make sure the radiator is not blocked causing a lack of circulation of both water and air. This may have been the cause of the initial overheating.