By the time I found a resistor small enough to keep the voltage at something the regulator could work with (100R), I found that my actual current draw from the Mega is on the order of 70mA. Power = I^2 * R == .49W ... which is bad juju for a 1/4 W resistor; heck I'd probably be burning myself on it if it were a 1/2W resistor.
Lower current draws from before were because the current would rise, drop the voltage below nominal, reset, lather, rinse, repeat. Even if I went with a 50R 1/2 W I have around here somewhere, I don't think that would be good either.
So yes, the zener was a bad idea.
I'm just going to hook the 15V to Vin and have done with it. At least it's within the rated spec.