As Ricrard states, all/any of his conditions can cause your problem.. the main reason I am leaning in the aux fan / overcharge possible is b/c you do not seem to have the problem until you loose airflow from a non-moving vehicle/traffric/idle condition .. that points me towards conderser airflow vs. blockage drier/lines/etc. .your comp. cut-out seems to be the RESULTS of high pressure run away due to lack of airflow...but, the test wll tell the tale.
If the fan circuit verification test passes, then you may also want to look for debries between the cond and radiator...but fan jumper sw test is still top of my list..you mention seeing fan at hot engine, but I think you are mis-interputing that as FAN OK, not realizing that coolant high fan has NOTHING to do with a/c LOW FAN operation..two completely different circuits that just share the same fan motor. LOW FAN jumper test must be done to verify the electrical intergrity of that circuit. If no low fan with that test, you could have a problem as simple as a fuse or burnt wire at the resistor.