I'm glad you managed to play SRIV again but I didn't quite understand what you meant by this. If you tried to run it via Steam, it always loads the "Saints Row IV" folder located in steamapps. But if you meant that it ran the updated SRIV even without Steam enabled, that's quite odd... I can't really explain it.
By the way, don't bother with backing up the Re-Elected version. If you delete it you'll be perfectly fine, and in case you want it back for some reason, you can just verify the integrity of the game's files on Steam and it'll download the new files with no problem.
I had two folders, one "Saints Row IV" which was the update game and a copy folder called "Saints Row IV Copy". Then i did the whole process you posted before to downgrade the "Saints Row IV Copy".
But everytime i tried to run the exe from the downgrade "Saints Row IV Copy" folder, instead it would run the Updated SR4... not sure why, but i'm guessing it has something to do with steam Folder name check or DRM.
But once i swapped Folder names between the two, "Saints Row IV Copy" > "Saints Row IV" the downgraded game ran fine.