Brit312, you raise some interesting points.
However, it is a matter of fact that neither No 1 nor No 2 engine ingested any tyre material. The engine surges that they experienced were due to a disruption of the airflow caused by the hot gasses from the fire. No 2 engine subsequently recovered and was producing useful thrust when the crew shut it down at the point of rotation.
Regarding shutting down No 2 engine, in my 33 years of aviation (30 of them flying) no aircraft that I have flown, or airline that I have worked for, allows for the shutting down of an engine because of a fire warning between V1 and Vr.
It's just simply not done. In my experience, if you suffer an engine fire after V1 but before Vr, you always wait until you are climbing away at a safe speed, and the undercarriage has been selected up, BEFORE you shut down a failed engine.
regards