Since you seem to have a fair number of JPanels, I don't think it would be a good idea to convert them to JFrames, since that would clutter user's dektop (who wants to run one application and all of the sudden find their desktop filled with 6 or more new windows ?).
So the "JPanel" choice seems logical.
Still, in case you want to give your users the option to customly arrange those panels (e.g. overlapping, side-by-side etc), then JDesktopPane might be a nice solution.
(Also, take a look at the relevant section of the Java Tutorials.)
Not directly related to your question, but having such huge classes (5000 lines without functionality...) is not considered a good coding practice (if not anything else for maintanability reasons).
From Oraclre's Code Conventions for the Java Programming Language, section 3 - File Organization:
Files longer than 2000 lines are cumbersome and should be avoided.
So, it might be a good idea to try and break it down into smaller, more reusable and maintanable pieces of code/classes.