(1) Engine failure, initial deceleration from Vy over a period of seconds while the pilot says "oh f********" slowly, then pitch to target turnback speed.
(2) Roll left to 45 degrees of bank whilst maintaining target turnback speed
(3) Change heading through 45 degrees.
(4) Roll right through 90 degrees to 45 degrees right bank
(5) Maintain 45 degrees right bank and target turnback speed until approaching runway centreline
Are you sure this would be the right approach? As far as I can see, during steps 1-4 and halfway through 5 you are still flying away from the runway.
Personally I would turn back towards the runway immediately (into the crosswind to minimize offset), and correct for the offset only at the end of the maneuver. So the teardrop shape is reversed.
Considering that you are going to lose altitude for sure during all this turning, I think that gives a better chance of making the threshold. Especially if the runway is short and you used the whole length during the take-off run. And in any case, I'd rather go off the far end of the runway at taxi speed, than undershooting the runway at flying speed.
Furthermore I think steps 1 and 2 should be combined. You drop the nose while rolling into the turn. So that by the time the nose is in the appropriate glide attitude, you are already established in the proper angle of bank and can start pitching for the turn straight away. (If you assume that this is essentially a ballistic maneuver it's relatively easy to model.)
In fact, Mark1234s experiment suggested that during this stage you can actually bank to 60 degrees, pull to the edge of the stall (not with 2G - it will be less but that's OK). Because you're not pulling 2G the nose will drop. At the time the nose has dropped to the glide attitude, you roll out to a bank angle that's sustainable, given your attitude, for the remainder of the turn. (Probably around 45 degrees.)
But I admit that that last maneuver will probably be an incredible bitch to model mathematically. And I doubt whether it would be the right technique to teach to low-time pilots in any case: If you don't roll back to a sustainable angle of bank at the appropriate time, you set yourself up for a major stall/spin accident. But that roll back might well be counter-intuitive to somebody without aerobatics/unusual attitudes experience.
Worth doing I think. I think I'll do it and open it up to collaboration (and shared blame or glory as appropriate!); I can certainly bring three aeroplanes (a modern 4-seat low wing, a vintage high wing taildragger, a microlight) to the party and can think of a few fellow flying researchers who'd enjoy joining in. (Pilot_DAR, India-Mike, any interest in playing?)
I'm not a test pilot but I find this sort of stuff fascinating. I would not mind bringing the R2160 to the UK for a weekend so we can have a go in a basic aerobatics aircraft too - provided that somebody with some test flying experience is sitting next to me.