Yes I think that is how it's supposed to work on PS4, you need to download individual items once. When you reinstall the content will be automatically downloaded installed. There is a menu to display the installed content for each game, but I'm at work and don't have access to my PS4 now.
I'm...
In the meantime GIMX may be worth a try. It allows to control the PS4 over Bluetooth, from a Linux computer. The Teensy 2.0 (required only during pairing) and — if needed — a proper Bluetooth dongle shouldn't cost more than half the price of a TitanOne.
The instructions on the wiki could be...