No, overfilling wouldn't cause an issue with damage the the cylinder heads, or the cooling system itself. Water isn't compressible, but air is. So the empty space of air inside of the cooling bottle can shrink and expand as the coolant expands and retracts with the heat cycles. If by chance you were to overfill the bottle and didn't give enough space for the coolant to expand, or even no space at all, it wouldn't hurt the system. That's because the Radiator Cap acts as a fusible link to prevent damage. As the pressure built up and pressed against the cap, it would slowly vent out coolant steam until the pressure went back down. Given that it's a closed circuit system with an external expansion tank (not an external overflow reservoir), you'd probably have to burp it after that to let some air in. But the fluid level should never change. We have an '07 F150 still running it's original coolant (I plan on flushing the system later this year), and for the 7 years of which we've owned it, the coolant level hasn't once dropped below it's cold level.
But when you say ⅓ of the way, are you saying that the coolant level dropped below ⅓ of it's capacity? Or that you simply keep adding ⅓ of coolant each time? As long as you keep the coolant about ⅗ full inside to cover the bottom, and to let the bleeder return pour in unobstructed, you'll be fine.
Quick question: Does your windshield ever get really greasy on it's own?