Don't buy a digital, you'll litterally waste money. I had the same issue. It's annoying but all you have to do is uninstall ff then download the trial and your digital hw copy again, basically this circumvented inserting the disk at all and because you already have the licenses it realises it's the full game.

Trial download is necessary because it's still the full ARR download but psn won't acknowledge you have a license to download the digital ARR without the disk.

I've been playing for the last 6 months now without the need for a disk, the only pain is unistalling and having to redwonload all patch files etc.