Couldn't find anything related to this anywhere else in the forums, so posting here in case it helps others.
I was having difficulty getting my controllers to work correctly in almost every game opened through the Epic Games Launcher.
The following workaround makes them open with Steam instead, using Steam's controller settings. I've only tried it on 9 games, but it's worked perfectly on all of them.
Install the Epic game and import into Launchbox if you haven't already done so
Open Steam. At the bottom left of the window, click on Add a Game > Add a Non-Steam Game
Click Browse, and select the .exe of the game (eg. C:\Program Files\Epic Games\CatQuestII\Cat Quest II.exe)
If the Add a Non-Steam Game window isn't showing, use Alt+Tab to bring it back, then click Add Selected Programs (you can add multiple games at the same time)
Right-click on the game in the left hand pane of your library tab, and choose Properties, then under Launch Options, type -epicportal (this allows the game to run without opening Epic)
Right-click on the game in the left hand pane again, and choose Manage" > Add desktop shortcut (you can delete this after you get the URL)
In Windows File Explorer, Right-click on the desktop shortcut, and choose Properties
On the Web Document tab, copy the entire URL (it should look something like like steam://rungameid/12345678901234567890)
Back in Launchbox, right-click on the imported Epic game, and choose Edit > Edit Metadata/Media
Select Launching on the left hand side, and replace the Application Path with the the Steam URL you copied, then click OK
In LaunchBox, it will say Install instead of Play, so you have to click it twice. No issues in BigBox as far as I can tell.