Desperate Over Heating Probs

It would help if you mentioned the model year of your Mustang. There are slight differences in how the fans are wired between the MY's.

Did you confirm that the fan works on BOTH speeds? How do the fan bearings feel?

Does the motor actually overheat?

But in my experience when the heater suddenly stops putting out, this means there is air in the coolant. Since the SOHC motor is generally self purging, after several hot/cold cycles if there's still air in the coolant, it's coming from somewhere. The usual somewhere for the SOHC is a head gasket leak.

There are kits to test the coolant for combustion byproducts in the anti-freeze. Consider performing a coolant system pressure test.

As for other things to check, look for a clogged exhaust. The usual cause is rotten cats.