With @Siguza's help, I found a variation of the launch command that worked. The only broken part was correctly invoking Java. The find command Sugiza suggested is below.

find /Library/Java -name java

That command returned the following results:

/Library/Java/JavaVirtualMachines/jdk1.8.0_65.jdk/Contents/Home/jre/bin/java

/Library/Java/JavaVirtualMachines/jdk1.8.0_65.jdk/Contents/Home/bin/java

/Library/Java/JavaVirtualMachines/jdk1.8.0_40.jdk/Contents/Home/jre/bin/java

/Library/Java/JavaVirtualMachines/jdk1.8.0_40.jdk/Contents/Home/bin/java

/Library/Java/JavaVirtualMachines/jdk1.8.0_101.jdk/Contents/Home/jre/bin/java

/Library/Java/JavaVirtualMachines/jdk1.8.0_101.jdk/Contents/Home/bin/java

/Library/Java/JavaVirtualMachines/jdk-25.jdk/Contents/Home/bin/java

As mentioned in the SO post about not finding Java, the path needed for --jdkhome ends with '/Contents/Home' and not with '/bin'. Here's the command that worked.

/Applications/NetBeans/netbeans27/bin/netbeans --jdkhome /Library/Java/JavaVirtualMachines/jdk-25.jdk/Contents/Home --userdir ~/NBUser --cachedir ~/NBCache --fontsize 16