Can't imagine having a data cap. Here in Portugal all ISPs offer 30mb, unlimited, with more than 100 channels and free calls in fixed phone, starting at 25 euros. I pay 50 euros for 100mb and 180 channels and also a mobile card.
If you wouldn't use your 250gb data outside of downloading ps4 games, I would just find a way to fix the PS4 laser so it install games very quickly again, or buy a new one. 80 euros times 5 months is 400 euros which is more than a new PS4. You can always sell your old one. Extra 80 euros per month for just 250gb (that would be what? 5 to 6 games?) is too much.