Maybe I'm misunderstanding, but when you're bleeding the system of air, the only real way to get all the air out of the system is by allowing it to circulate, which means the thermostat has to open up. This will allow the water pump to flow the liquid through the system, allowing for the cooling. With the radiator cap off while the thermostat is open, water will come out of the top, mainly because you're dealing with pressurized coolant finding an open space.
The way I flush/fill coolant is I fill up the empty radiator with my 50/50 mix until I hit the top. Periodically, I will squeeze the upper radiator hose and "burp" the system to help get out some of the air. When I can no longer get any air out of the system that way, I then start the car with the radiator cap off and turn the heater on full blast. I will watch the level of the coolant at the top of the radiator cap and wait until the coolant level recedes. It will take a bit for the car to get up to temperature, but when it does, you will know it. If there are any air pockets left, the circulation of the system will find them and push them out of the radiator cap opening. If the level of the coolant sinks, put more coolant in there.
I've never had a problem doing it this way. I've been successful 100% of the time using this method, and I've used it on anything from small cars to Peterbilt big rigs. There are other ways to do it, but it's like shaving: everyone has a preferred method.