Before you write me off, please consider that neither of these are answers to my question:
Use Oracle Java instead of OpenJDK for now. You can pull that in through WebUpd8's repository.
sudo add-apt-repository ppa:webupd8team/java &&
sudo apt-get update &&
sudo apt-get install oracle-java9-installer
It doesn't look like this is going to work with OpenJDK, so if you want to play with the latest and greatest Java, this is going to be the way to do it for now. Otherwise, from what I've seen, you've done this correctly and once this gets actually fixed, it will work just fine.