I think $800 sounds pretty good, but only if it feels right to *you*. You are the one who has had to live with the frustration and inconvenience.
In fairness to the landlord, it sounds like they did 'try' to have it fixed. If you feel the repair efforts were not really 'quality' attempts, i.e. if it just seemed like they sent repair people to shut you up, then the case might be different.
But, if the apt. was new, it would have been to the landlord/owner's interest to have the repair done properly the first time. Repeated water damage doesn't do the apt. any good, that's for sure. So the repair efforts were probably well-intentioned.
The roof leaked at my school from the very beginning. The carpet in some classrooms would get completely soaked with every hard rain.
It's the roof guys that did a sucky job during construction. They should be the ones responsible for their bad work. Same wrt your apt., it seems to me.
So, if $800 feels right to you, I'd take that and be happy. Believe me, you don't really want the stress of lawyers. Life's too short for that. Just my opinion however.