Well, after various attempts of mechanomagics, I managed to get the game running by using the command prompt, heading to the Steam folder for Medieval 2 and typing in
start kingdoms.exe @mods/americas/TATW.cfg
To get the Steam window for M2TW pop up, from where I picked the Americas campaign.
The game now runs up to the start of the Third Age campaign, from where it crashes to the desktop with a error message telling there was a "unspecified error" (apparently some form of national secret since I can't be informed of its nature).
So, any solutions for this particular issue now?