obviously, I want my applet to work with as many versions as it can, (I do, right?)
I disagree. It is well known that running Java in the web browser is a security nightmare. The best approach (for your users' security!) is to not use applets at all. But if you must do it, then you should be aiming to do it as securely as possible. That means writing your JNLP file to insist on a recent version of Java. Preferably, the most recent patch level of Java 7.
But to answer your Question, the simplest test to find the oldest a version of Java should support your application is to attempt to compile it with that version of the JDK. If it compiles on an old version JDK, then it is fairly likely that it will run.
But then you should test it, because successful compilation does not guarantee that the application will run properly.
And as @Lonzak points out, there is a separate issue of whether the user's installed Java supports JNLP.