I was stationed at Minot AFB and one of our B-52 ran into a flock of geese, (hey guys its fall and bird migratory season), during the fall migration. There was a great deal of damage and two of the B-52s engines were taken out. fortunately the B-52 had 6 more but I remember talking to the crew afterwards and they said that the recovery was dicey because they were flying a low level bombing route. But, and this is the important part, they were already airborne. Since takeoff and landing is the most critical aspect of flight it's not surprising that the crew of AA 587 was unable to handle the emergency.
The post with the picture of the wildlife refuge shows that the bird strikes might have happened before the end of the runway and that the engine shredded and parts of the engine knocked the vertical stabilizer off into Jamaica bay at the sw corner of the refuge then the timeline is fairly straight forward.
Let the accident investigators look at the forensics. Put the tinfoil away.