So if I'm reading what you wrote correctly (and you aren't making it easy on us), you ran the car with the heat on and radiator cap off, filling up the coolant as the car was running. In addition you installed a new thermostat and correctly routed the overflow hose to the overflow reservoir. That all sounds good to me.
The "toilet flush" you are describing is the thermostat opening, which is a good thing. That means you installed it correctly, and it is opening. At that point, you should let the car run a few more minutes and make sure the coolant level doesn't drop again, as coolant running through the system may fill pockets in the head and block that weren't getting coolant with the thermostat closed.
Everything you said sounds good, and completely normal. But, what about checking for a leak? I doubt the thermostat was the problem judging from the symptoms you initially described. Is the system leaking? Is your floorboard wet? Did you get a coolant pressure tester and check for leaks like we told you to? If there is a leak and you are constantly overheating the car, you will inevitably damage the head, or worse.
Edit:
An important note, all the things you said you did will never put the cooling system in a state that will allow you to really check for leaks. Meaning; with the radiator cap off, the system will never become pressurized even at operating temperature, and will probably never leak. What you should do at this point now that you have the system full and free of air, is put the cap back on and let the car run to see if it leaks. That is, if you didn't get the pressure tester like we told you to. In that case, you should let the system cool, and then check it with the pressure tester.