Look for where the cat/dat files for the mod are, and then look in the x3 root folder. You will see another bunch of cat/dat files in there that are numbered.
Take a note of the highest number, and then go back to where the mod files are installed. Rename the mod files so that they are numbered 1 higher than the highest number you saw in the x3 folder (I.E. if the number was 11.cat/11.dat, then rename the mod files to 12.cat/12.dat). Then move the mod files to the x3 folder. Start your game as normal.
PS. when you use the false patch method you don't have to select a mod in the mod list from the games launcher.