Well, let's all trash Cosmo for a sensible question eh?
Yes, Cosmo (and welcome here, by the way), I'm not sure of the exact attempts made by the crew (if any) to try a relight, but at the speed they were at they would have needed an APU to do it, and it is a slow thing to start when you REALLY need it. I actually think it could make a lot of sense to keep the APU running a bit longer after departure. Who knows whether a shutdown and relight MIGHT just clear an engine that has choked and spluttered to an early grave with bird debris? We are only talking around 30-50kg of fuel I guess. It is certainly the correct procedure for flameout due to Volcanic Ash ingestion. Certainly something worth bearing in mind and, as they say - 'Captain's discretion' rules the day.
Now we can both be ridiculed