JN
The circumstances you mention were all contributory factors but none in isolation precipitated the accident.
- The overweight issue generated by ATOW together with the tailwind and some 'hidden' fuel.
-The CG position being aft of the optimum
All served to make the handling of a single EFATO at it's most demanding - Although probably not outside the capability of the aircraft.
The pilot did not use full rudder to control the yaw - we don't really know why but it was not a causal factor.
The F/E evidently (uncommanded) did shut down a poorly looking but still running engine at or about Vr. Subsequently the other engine on the same side failed.
2 engines out on the left means no gear retract, means no acceleration, means they were dead from that moment on.
Go bless 'em