So I'm re-reading this thread and these two things jump out at me.
1. Your fans do not turn on when things get hot. Improperly working fans would sure cause a stopped car to overheat. You could have a bad thermosensor or a bad fan motor (a long shot is your fan blades could be sheared off at the motor, it happened to me), possibly the radiator is bunged and the thermosensor is not getting good coolant flow so isn't signaling properly. Maybe one of our wiring experts could suggest potential components that might need replacing.
2. You can't bleed the system because the coolant isn't flowing. That screams restriction to me. I'll return to the flush. I know that you've checked the flow of various components individually, but have you checked the flow of the entire system after it's all put together with the t-stat out? I would do that.
Finally, it sounds like this is an intermittent thing, so that would suggest an electrical malfunction. I'd take a hard look at the fans and assorted relays, sensors and switches that run them. Also check the resistance on those fans. Make sure they are working well.
Keep us posted.
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