That's pretty much what you need to do, is just overlay the old files back. If you look in the news forum, there are zip files with the updates for each release linked at the bottom of each release notes, so if you get the one for 1.013, then that will function.
Bear in mind that savegames from future versions of the game won't work in order versions of the game in most cases. You can open up the save file and change the version number on the first line (but make sure you make a backup of the save file first!), and usually that will work. However, if loading that save file in an older version then gives an error, then there was a non-revertable change in the given release. Sometimes that happens, but it's not overly common. I can't remember off the top of my head if 1.201 has any of those compared to 1.013.
You can also revert to prior prereleases, so if you were liking one of the beta versions but not the most recent one, you can even more easily just revert to that and then the savegames are less likely to have issues.
