However, the manager tells me that KJFKv2 is ACTIVE but not installed..... How can that be, as I reinstalled that scenery just a few hours ago???
Not installed means "not installed in the Scenery Library" so, fact you have the files, doesn't mean it's installed in the Scenery Library.
Of course, our installer WILL put it in the Scenery Library which, in case of P3D 4/5, means it will create an add-on.xml in the Documents\Prepar3d V5 Addons, and activate it. So, under normal circumstances, when you install using the installer, it will be installed.
But, since in both the previous cases, it seems you either installed something very old or removed something manually, or both, I cannot possibly tell what other problems you had with JFK V2, which caused an incomplete installation, which never happens normally.
Reinstall JFK and pay attention for any errors. And check if the add-on.xml for it has been created ( it always does but, with your system, everything seems to work strangely... )