I, for one, Obie, very glad not to be with your airline. Nothing "rushed" in my entire career, normal, non normal or in regular comp exercises. T/O, engine failure, drills complete, land as soon as. Very simple for the reasons expresed many times but still appear to be wooshing over your head. If your airline gives a hard time to a Captain for "flying the aircraft", cognicent of his mayday situation, operates in accordance with approved procedures, "your" airline looks to looked at very carefully. Maybe "your" airline does not approve of standard Boeing procedures which were written for airmen across the regions. They were written for simplicity, ready understanding and if followed would almost certainly lead to a safe outcome.
In my airline, there would be vigorous investigation of anyone not following the above. Some of the reasoning you give for not adhering to well defined procedure would have us showing you the door. Circling about, on one, which might also fail, burning off fuel because a possible single-engine GA at heavy weight worries you...............er, .........worries me.