Where do you get the idea that you have to pay to package the JVM now? OpenJDK and Oracle JDK are now identical (they already have been pretty much for years now, but Oracle recently worked to open source any remaining bits). There are vendors all over the place you can now get a free JVM to ship with. AdoptOpenJDK being an obvious and neutral one - https://adoptopenjdk.net/
Processing 4 is already embedding OpenJDK as far as I know. Processing 3 works fine with it, as long as you ignore the very daft warning message!
EDIT - incidentally, if you want more information on all this, check out the Java is Still Free post from Java Champions - https://medium.com/@javachampions/java-is-still-free-2-0-0-6b9aa8d6d244