I do want to warn you, even a tiny drop of freon in your eye causes instant and permanent blindness. The system is under a LOT of pressure even when it's low on freon but I'm going to laugh pretty hard if in the end it turns out your system is low on freon because I can tell you all this hours of intricate labor discussion isn't doing a dang bit of good until all the simple things have been diagnosed off the list, you don't know what the problem is, we start with the easy stuff, otherwise we might as well plan a trip to the moon. Chances are good that to replace that stupid actuator door you're going to have to pull the dashboard and remove the whole big bad $500 box and take it apart much like you would if you were replacing either heater core or evaporator, which is why they quoted you $180 for the labor, proper tools and know how it will take the experienced mechanic two hours, but you do it yourself and you can plan the entire afternoon. Now get yourself a set of gauges to measure pressure on low/high side of the a/c system, then check that your system has enough pressure. That's always the first thing, when the system isn't cooling, make sure it has freon and that it is cycling like it should.