There has to be a flow issue, your diagram is confusing but is your heater core inlet a t'd connection? The diagram looks like it is, and if this is true and runnin back to the water pump than problem solved as said earlier coolant will take the path of least resistance and flow straight back to the wp.Are both heater hoses hot? I see you have a flush t in the outlet, I am betting you can run the engine with the cap off it and it doesnt have alot of pressure/flow. Can you better describe/show the layout of your cooling system?
The heater core is basically a mini radiator, blower motor is its cooling fan, if you dont have flow of the 190* water it doesnt take long to cool that small amount off that the core holds especially if its half plugged. I agree with what others have said, compressed air wont do a thing when flushing any kind of radiator.