Greetings and thanks for your efforts!
My Documents are relocated too (D:/Разное/Мои Документы), and i have Russian localisation. FAF usually places all my downloads (maps, mods, etc.) to it's Program Data folder (for example, maps are in C:\ProgramData\FAForever\user\My Games\Gas Powered Games\Supreme Commander Forged Alliance\Maps).
Seems that all these were reasons for my "dances with tambourine".
1st, your last version of installing bat can't manage spaces ( ) in my folder's name ("Мои документы"), so it created a folder "Мои" and used it as My Documents folder, unpacking there all contents of "fa" folder.
Also, i placed maps to FAF Maps folder in Program data.
2nd, after placing "fa" folder to documents, and 2 other files to their destinations, and also deleting prefs file, i started game with "Coop" label. But game didn't find any coop maps, old (x1ca_coop_001.v0011) or new. It crashed after i opened preferences and pushed button "Random map" (with empty map list, of course).
I got tired of fighting with all that, so I attach a pair of log files. Good luck.
Maybe I'll test later in specially created "English-languaged" profile.