It is definitely a "registry" problem. I had the same problem. The .exe livery installers claim that no sim is installed. By looking at various releases of FSLabs over time, I found that the new releases don't seem to include the "uninstall" entries. Believe it or not, these "uninstall" entries are required for the livery installers to work properly!!?! :o :o
I created a full set of registry entries. You can download here: https://modsfire.com/7F6X390VWT48ygw
NOTE: the uninstaller stuff is in the "FSLABS 2.reg" file.
These files have all the needed entries for all the variants (A319, A320, A320SL, A321, A321SL)... it's setup for the "5.0.1.187" version, but you can easily edit as required if you want... and as per the readme.txt you need to edit "FSLABS 1.reg" to set the correct locations as per your install.
You could use inibuilds liveries you just need to download "base" texture pack and you are good to go, this issue you got here is clearly registry problem.