Blind Pew, so many inaccuracies and assumptions it’s difficult to know where to begin.
The 744 was designed by Boeing to be able to continue to destination OEI if certain criteria are met. The FAA mistakenly threw their toys out the pram, presumably because those involved had twin engine experience. There was a rumour part of their motivation was because not many quads were operated by US based airlines they wanted to level the playing field and remove the advantages provided by having four engines. Whether that rumour is true I have no idea. They subsequently wound their necks in once shown the Boeing FCTM.
Just FYI, all BA 744’s had real time remote engine monitoring by both RR and BA power plant with many more parameters than available on the flight deck, and a remote health check of the remaining engines was also possible (and more than once on the 744 I received an ACARS about a possible issue before it was apparent on the flight deck). I wasn’t on board but I suspect the crew knew exactly why the engine failed and how healthy the remaining three were. 744 crews were trained to continue while gathering information and decision making in the knowledge that a return or diversion were always options.
The decision to continue was justified, within the rules and safe, the issue with fuel balancing that meant the crew ended up in Manchester was unfortunate but the BA change to the procedure was Boeing approved. For your information there was no fuel shortage, however the crew found they were unable to move some of it to the tank they wanted it in so decided to nominate it as unusable.
Despite being shown references, I don’t doubt you’ll continue to disagree.