I realized this when I launched the game, and the game automatically created a new Skyrim folder (the importance of this comes in later).
So what I did: try system restore; this did not work. My computer, for some reason, has decided to delete any and all previous restore points, including ones I had manually made.
What I did next: install recovery software. I tried two different softwares, and both found many of the files I had removed from the recycle bin. The Skyrim saves were not among those files. Could this be linked with the fact that Skyrim created a duplicate of that same file in my My Games folder? And that is why the program cannot find the one that I deleted from the recycle bin?
Lastly: is there any other method in existence to recover those saves?