ChrisVJ
With a single-engine jet you do not have much time if the engine fails on take-off. Unless it has taken a bird or surged for some other reason such as ingestion of efflux from another aircraft, engines do not tend to just stop working without a mechanical issue or major interruption to fuel flow, in which case relights/restarts are very unlikely to be successful. You might have one shot at a relight depending on your height and speed at the time, but the presumption is for an ejection. This is true whether you are in the Snowbirds, Red Arrows or Thunderbirds - they will clear the formation first because a collision is the most immediate threat, and all the teams have planned and practiced formation escape routes for just this reason.
The zoom provides height (separation from the ground) and more importantly a positive vector for the seat, the time and airspeed elements are secondary. The critical factor in escape is the overall seat vector. Ejections from the same height, attitude and airspeed but with different vectors will have different outcomes in terms of apex and chute deployment. You are correct that attitude plays a big part at lower levels and there is no need for persuasion - an inverted ejection from 100ft is not likely to succeed whereas an upright wings-level at same height will. In this accident, ejections within a few seconds of the power loss would probably have succeeded, but we will never know for sure.
Some years ago an instructor on the Jet Provost had a birdstrike and engine failure but spent so long trying to re-light and making his MAYDAY call that the combination of height and rate of descent were insufficient when he actually ejected. He hit the ground in his seat and survived, but broke his neck when the seat tumbled across the field and was rendered quadriplegic. That accident was used to reinforce the teaching on 'zoom and boom' unless you had made the gate of 600 ft or 160 kts.