Well, I didn't give up. I was going to download the DLCs separately but decided to attack this first from another angle
I want to share this in case that anyone here has the same problem.
This procedure applies to games like GOTY versions or Complete editions where the DLCs are released as an additional disk separated from the main game.
Here is what I did to make it work:
1. Use ISO2GOD to convert Disk 1 (the main game) to GOD format and transfer to the XBox 360 as usual.
2. Use Xbox Backup Creator or any other tool like it to extract disk 2. Do not convert it to GOD. Look into the extracted files and find the folder CONTENT\0000000000000000\FFED2000\FFFFFFFF\. This folder contains all the DLCs.
3. Transfer all the contents from this FFFFFFFF folder to the Xbox into HDD1\CONTENT\0000000000000000\(GAME_TITLE_ID)\00000002\
4. Play your DLCs
The problem in my case was that at the beginning I had converted Disk 2 to GOD. I got also confused by the FFED2000 folder when I later decided to use Xbox Backup Creator and I was just using it instead of 00000002. That folder structure must be totally ignored.
The option to play the DLCs got finally enabled on the main menu.
I hope this help others.