Would be nice to know what happened to repair it.
The info you provided was good, It should be fixed by now.
Just my opinion, That system should have shut down before icing up that way.
Most systems look at High Pressure for safety cutoff, But if it is low on refrigerant it can run forever, and is very well Cooled.
Hope to hear a report soon.
Theory only works perfect in a vacuum.
If you burn up the compressor (even if the part is under warranty), you still won't like the bill if you are paying for labor.