Ok I figured this out, so I figured I'd update this for anyone else wondering how to pull their saves from the other platform.
The other platform has their saves located at:
C:\Program Files (86)\ $team\ userdata\ (long number different on every machine)\ 241930\
Inside will be a folder named "remote", which contains the gamedata.sav, and a file named remotecache.vdf. Copy the contents and then paste them in the following location:
C:\ users\ (your machine name)\ Documents\ WB Games\ Shadow of Mordor\ Saves
So in the $team folder it had a file named "remote", which had the gamedata.sav inside and then outside of that folder remotecache.vdf. I'm not sure if the GoG save files work differently, but I put the remote folder inside the save folder along with the remotecache.vdf and then copied the gamedata.sav file from the remote folder and pasted it inside the saves folder. I had a GoG save from starting it up after installing it and before I figured out where the saves were and that was not inside a remote folder. I'm not sure if that has something to do with the other platform's cloud saves and if the GoG version will work with the remote folder. I didn't try it, but it's possible it will work I just thought it was easier to copy the 1,024 kb file and have it in two locations than starting the game a couple times to figure it out.
I hope this helps anyone else that decided to get the DRM free version and switch.
Have fun!
Post edited September 03, 2022 by Gylfe