Someone who has been successful can chime in, but looking at the DB it looks like the reason it doesn't work is that the Advanced weapons are not actually in the same tech category as the normal versions, so they won't show up in the drop-downs. There is also no distinct component type for the Advanced weapon systems in the relevant DIM_ tables.
To make these work, again someone else can chime in with what has worked for them but the approach I would take is to modify the FCT_TechSystem table and set the TechTypeID of the Advanced techs to the same as the corresponding normal techs. For example, the Advanced Laser Focal Size techs have TechTypeID 148, while the normal Laser Focal Size techs have TechTypeID 15. Changing the former to match the latter should allow you to use both tech lines to design lasers.
As one such successful individual I can say that this is correct. By changing the advanced variants tech type to be the same as the standard variant you can make the game add the tech to the drop down and use the weapons just fine.
The only exception is the advanced railgun which needs some extra work. Since you have changed the tech ID type to be the same as the standard railgun, the game will think that your advanced railguns are just normal railguns and give them a shot count of 4 when it should be 5. You can fix this but it pretty much means that for every advanced railgun you design, you need to correct the shot count in the DB to be 5 (or whatever it should be if reduced size).
