My assumption is that they tried to land, found the runway occupied by a bird
Sounds like the normal symptoms and reaction to a bird strike. Go-around, shut down the affected engine, and land on one engine.
Not so sure about the 'normal'; why not just land. Better to be on the ground with a thumping engine than in the air. Was this indeed on approach? Remember RYR in CIA?
I now read in the MEN that indeed it was inbound from BCN. I wonder what height it was on approach? I still think I'd land the bird.