I think I've figured out a solution to the problem. In posting this solution, I am hoping that someone out there will either realize what I had done wrong with my KDS installation, or the KDS team will see something that is a possible bug.
Ultimately, it looks like the .project has incorrect values in it. When I opened the .project file after importing ksdk_platform_lib_K64F12, it had entries like this:
<link>
<name>platform/adc16/drivers/fsl_adc16_common.c</name>
<type>1</type>
<locationURI>PARENT-4-PROJECT_LOC/platform/drivers/src/adc16/fsl_adc16_common.c</locationURI>
</link>
I haven't been able to figure out what PARENT-4-PROJECT_LOC refers do, but I do know from the Eclipse documentation that environment variables are allowed. So therefore, I should be able to use this:
<link>
<name>platform/adc16/drivers/fsl_adc16_common.c</name>
<type>1</type>
<location>${KSDK_PATH}/platform/drivers/src/adc16/fsl_adc16_common.c</location>
</link>
But that didn't work. After more digging, I found out that Eclipse doesn't support environment variables like this by default, but instead it has a feature called Linked Resources that can be used to support path variables. You can find this in Window -> Preferences -> General -> Workspace -> Linked Resources. I modified mine like this:

After I added that and reloaded my project, bingo! The file I located with ${KSDK_PATH} could now be opened in the editor.
It also turns out that if you make this modification to the "master" .project file found in the KSDK folder and then import it, the imported project works straight away.