Okay, here's what I did, don't know what part made it work:
I downloaded and extracted the new listener .zip to a new directory.
With the current listener (1.1.3) running, I backed up the apex-config.xml file.
Started a command line (I'm on windows), cd to the new listener's directory, and ran the java -jar apex.war command.
it said "Migrating existing configuration in <apex-config.xml directory>\apex-config.xml to the latest format,
Enter 1 to enter passwords for REST... I chose 3 (skip)
Enter 1 to migrate existing Resource Templates...I chose 2 (skip)
Enter 1 if you wish to start in standalone mode or 2 to exit...I chose 2 (exit).
Then I re-named up the apex.war file in my weblogic apex listener's deployment directory.
Copied the new apex.war file from the new listener extracted directory to the weblogic deployment directory.
Launched the weblogic console, and updated my apex listener deployment, then activated changes.