After experimenting with the new KSDK and the KDS in various versions, as well as testing IAR with the KSDK, I've determined KDS and the KSDK is just a little too unstable to using going forward yet. Particularly the debugging in KDS seems buggy.
So I've switched back to CodeWarrior 10.6 and the new MQX 4.2 (which includes the features of the KSDK I needed). However, I've run into something strange:
In CodeWarrior 10.4 and previous versions of MQX, as well as in the KDS 2.0 and KDS 3.0, and in IAR, I can choose to use either the internal emulated J-link in the K64F with the Segger firmware(which I find to be a bit buggy and inconsistent), or an external Segger J-Link box plugged into the JTAG 10-pin connector on the K64F. The external box works in the other IDEs, and works more consistently than the emulated J-link.
But with Codewarrior 10.6 and MQX 4.2, I can't get the external J-link to work. It's LED flashes red, and the LED near the reset button on the K64F flash red, and it eventually fails. I also can't figure out how to enable the output from the debugger to display in a console in CodeWarrior, where it was on by default in KDS.