Unlike PS3 or 3ds, ps4 has meaningful updates which extend the sony api available both in the system and online. For example: 4.07 patches a part of the current hen workflow (I don't remember if it was the user or the kernel part, but I do believe it's the latter), 4.50 adds game installation to USB and 4.55 adds pro mode to deliver special graphic settings to ps4 pro.
Without these functions, syscalls, and underlying code base properly implemented the games simply will crash. Even if we force a game >4.05 to install (which is completely possible with the game's unencrypted files) it will just plainly crash into a ball of fire trying to run.
So, unless we manually implement those changes (via decrypting an update and installing) and then "spoof" (right down changing the version everywhere) there's a chance of that working. As I put it, it sounds more and more like updating to me.
Long story short: Wait for releases in newer versions. Maybe there's a chance of installing some sort of patch for the update code to ignore signatures so we could install "cfw"-esque updates of the system. I highly doubt it though.