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IHBD - if the heater core was leaking, wouldn't there be some evidence of that, like water on the rug on the floor inside the cabin as well as the odor of antifreeze inside the car, and maybe slowly dropping levels of coolant in the tank? The moisture from coolant on the windshield is usually slimy/sticky, not just water condensing on the cold glass.
Rocco's suggestion sounds more likely to me, especially if the car has been outside most of the time as opposed to being inside a garage where that crap would not constantly fall on the car and get past the screen by the windshield. Chestermo said this in post #2.
I tend to agree with you. If there were a slimy film on the windshield, then it would likely be a heater core issue. He'd be able to smell and almost taste it actually... I wonder if he has a blend door not fully opening/closing.
What hasn't been mentioned yet is that an iced-up evaporator can cause moisture to blow out of the defroster duct onto the windshield. Do you know if your Freon level is low?
There are other causes of frozen evaporator coils, as Google says --
An evaporator coil freezes due to poor airflow, causing the coil to get too cold, or issues with refrigerant, like low levels or a faulty metering device, which lowers pressure and temperature, leading to moisture freezing on the coil. Common culprits are dirty air filters, blocked vents, malfunctioning blower fans, refrigerant leaks, or setting the thermostat too low, all hindering heat absorption and causing ice to form.