Sorry, ITCZ, only just got back from a trip....
No, nothing in the manual, or the Boeing one. The 777 A/P shouldn't have a prob with this maneuvre - it's just a maths exercise for it, so I've been told. The L. a/p has been removed for evaluation on this occasion....
Agree with your comments on older Smiths a/p's and the cautions - absolutely correct.
As regards original topic: it's all about sit. awareness and politeness....