I just had great success in taking all my modified files (including the plugins folder, all of it) and putting them into a folder called "upgrades". I leave a copy of them in there on a permanent basis with the same directory structure.
Now when I upgrade, I unzip the new WP to the desktop of my PC, then I copy the contents of "upgrade" to that folder, overwriting any existing files in there, and then upload the whole kit and kaboodle to my server.
It was a painless up grade from the 126.96.36.199 to 188.8.131.52 where as before it was a lot of struggle.
I'd suggest this for anyone. Of course, if you make modifications to any of the other files, you have to include those in the "upgrade" folder or it won't work next time.
Just a thought.