Blocked Pitot Probe

It's winter, cold has $hit, sideways blowing snow and sleet the previous day and you walk up on to an aircraft and see flags on the airspeed and altimeter indicators.
  
     
  
You could say..... bad Air Data and swap them, but the problem stays on the original side???
  
     
  
Now what?

From previous experience, I know that this is a clogged pitot probe. I'm guessing (but I believe I'm right) that once the ice clog sealed off the pitot system, outside barometric air pressure went up. The Air Data now is sensing this higher pressure static air. So...... the Air Data expects equal pitot/static pressures on the ground and always higher pitot pressure than static while flying.

What do we have in the case of a fixed (clogged) pitot pressure that is lower than the now higher static pressure...... negative airspeed. The air pressure inputs are out of tolerance as far as the Air Data computes them, hence..... flags!!!

The first thing to try (which usually corrects the problem) is to just test pitot heat. The probe gets hot, melts the ice plug, pressures equalize, and the flags pull out of view.
  
     
  
Not in this latest case of ours. We did have water/ice in the probe, but we also had it in the pitot hose inboard from the probe. This is "not" a normal situation unless some dummy (me) put the Pitot/Static test box on it and blew the ice/slush plug into the hose by applying test box pitot pressure.

Either way, we took off the probe and used compressed air blowing from the Air Data hose outward to the probe quick disconnect.
  
     
     
  
What really threw us at the start was the fact that I applied 300 knots of airspeed to the system early on. When I dropped the test box back to 0 knots..... the airspeed indicator stayed high? Now I've got pressure that made it pass the ice blockage in the hose or probe, but it didn't fall when the test box was lowered. In other words, I've got pressure stuck in the hose.

The hose quick disconnects are spring loaded closed when removed from the Air Data (and in this case , the probe. Not all probes have quick disconnects). The Air Data side of the connection is open to ambient. I filmed the airspeed indicator as a mechanic disconnected the pitot line from the ADC. (Video below) 
  
As a note; during the air purge of the system, both quick disconnect springs had to be overridden to allow air to pass through the hose.