My opinion is that OP has a case.
The only thing extraordinary here is the delay - 6 hours.
BA have acted responsibly in delaying the flight, but as others have noted, they were sluggish in providing (any) corrective actions for passengers and it seems they were complacent in letting him endure a six hour delay. As others have stated, efforts could have been made to prevent this.
To rely on the fact that they could term this 'exceptional' seems like a 'cop out' and stubborn effort to not find an alternative - which is the key issue here. If anything, the lack of alternative offered would encourage me to make a claim as it makes me think they did not try their best to get him to his destination as close to his scheduled arrival time.