Got it running here by (kind of) following the instructions on their Discord. If you've run the GOG Fallout London installer, you should now have a "Fallout London" folder sitting right beside the "Fallout 4 GOTY" folder in Fallout 4 Bottle\drive_c\GOG Games.
I would recommend creating a copy of the bottle, because I don't think the original game will run after completing the following steps:
STEP 1:
Move the contents of the _AppData folder (found in "Fallout London" folder) into
Fallout 4 Bottle\drive_c\Users\crossover\AppData\Local\Fallout4
STEP 2:
Move the contents the _Config folder (found in the "Fallout London" folder) into
Fallout 4 Bottle\drive_c\Users\crossover\Documents\My Games\Fallout4
I didn't want to mess up my existing Fallout 4 installation, so I replaced the "Documents" symlink in
Fallout 4 Bottle\drive_c\Users\crossover
with a real folder (including the subfolders) before moving the files.
STEP 3:
Move all of the contents of the Data folder (found in the "Fallout London" folder) to the Fallout 4 Data folder in
Fallout 4 Bottle\drive_c\GOG Games\Fallout 4 GOTY
STEP 4:
Move the f4se_. files from the "Fallout London" folder to
Fallout 4 Bottle\drive_c\GOG Games\Fallout 4 GOTY
STEP 5:
Create a new program starter symbol in the Crossover Manager by selecting the "Fallout 4" bottle and running "execute command" with "Save command as program starter" checked and the command Fallout 4 Bottle\drive_c\GOG Games\Fallout 4 GOTY\f4se_loader.exe.
By doing this I got the program started and after creating my character i'm now at the beginning of the introduction quest. Maybe some of the problems described by others may still occur.
iMac Retina 5K, 27", 2020
macOS Sonoma 14.5
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