Hi GaryOlmstead,
There are a number of things in this post that I would consider problematic for the proper operation of the Kinetis specifically and for 3.3V CMOS chips in general.
What is the part number you're using for the power supply? I don't think I've ever seen the noise you're describing on a Switch Mode Power Supply or a charge pump supply. If you have a 600mV P-P pulses, you are at the datasheet maximum of 3.6 but I would definitely consider what you're describing as having a very high potential for damaging the chip. If the components are within .250" and 0804 then I wouldn't think you'd have problems - there's something else going on here. See my comment about power and ground planes below.
I think you're expecting that the abuse you could put on old 5V bipolar TTL parts through in terms of power supply noise, fluctuations and out of spec operation will not affect modern CMOS logic. Even something like a 5.0V NMOS 8051 or PICmicro would have difficulty surviving what you're putting into the MK60. I don't think a AVR would handle this at all. Regardless, for modern 32bit processors, you have to be pretty fastidious about power: but that's not that difficult or expensive to achieve.
What do you mean "power and ground are mostly on internal layers" - do you not have a single layer for each of these? How are you connecting/stitching between the power and ground areas? Nothing succeeds like a full PCB plane taken up by ground, followed by Vdd - if you don't know what you're doing you could have induced currents and voltages in what should be constant voltage rails.
You haven't mentioned decoupling on the chip - I recommend that you follow what's done on the Freedom/Tower board as a reference. That includes common mode chokes on Vdd and Vss.
Internal clocking should be okay but not if you're going to use USB or E'net in your application.
There MUST be a pull up (100k is fine) on the reset line and I would recommend a power line monitor to make sure reset is pulled low if the voltage gets below a certain point (I use 3.15V) as it provides a hysteresis delay between power good and reset high. I believe (and the NXP engineers can confirm) that not pulling up the reset line during power up will kill the chip (and, I believe will produce the hard short that you are experiencing) - I know it will on other chips.
The "soft" Zener is especially worrisome, if you see 4.0V on a Kinetis pin, then chances are you'll kill the chip (or any 3.3V part). The 4.0V is 'way outside of operating spec and appears to be sourcing more than 100mA of current (or else the internal pin diodes would pull the voltage down to 3.3V) which is more than the part can sink. This will definitely kill the chip.
I'm still happy to look at your schematic but I recommend you find somebody with experience with 3.3V CMOS logic to redo your PCB layout so that you have a guide for the future.
Sorry for being blunt.
myke