Hello cbwhippet,
This is no easy task, but with enough patience, time and reading you should be able to get this done. First confirm weather or not the applications are available for the latest version of Android by installing the games on your newer phone. Then you will want to head over here for a write up on transferring the save game data to the new phone. You should be able to complete this task without paying for the premium version of the app.
Let us know how it goes.