It's unlikely I'll eve be in your exalted position Jon, but I think you're being a little unfair to my countrymen there. Change in procedure for US airspace is not a 'tacit admission of a FU#$up' as much as they didn't know that US procedures differ from theirs, they now know that and are prepared to deal with it.
Speaking as a wannabe with very limited experience but a fair amount of enthusiasm I'd say that there's a considerable difference between a 747 Classic with one engine out and a 744 in the same situation, especially one with RB211s. Also, for all its facilities, I'd consider hanging around LAX with all that traffic in the area constitutes more risk than pushing forward, especially if you have Maintrol on the line telling you it's OK to do so. From MAN it's just a short hop to BA maintenance (and by extension Rolls-Royce) to fix the engine, something that would be trickier in LAX, especially given the compatively rare engine/airframe matchup that BA uses on its 744s.