'I was just thinking that pairing Alexei with either of his parents would have made him stand out in a crowd. I would try to set up the groups so as not to extract a great deal of notice.'
Precisely. That is why I would have three or more parties. It would make sense to pair Alexei off with someone other than his parents (I imagine that apart from Nicholas he was the most easily recognised of them, and unlike Nicholas, he didn't have a beard which could be shaved off!) However, I doubt whether Nicholas and Alexandra would allow their darling baby to go without one of them. You would certainly need to separate Nicholas and Alexandra.
Just for fun, here is my ideal solution:
Olga, Tatiana and Prince Vassili Dolgoruky as their uncle
Maria, Anastasia and one of the tutors
Alexei and the other tutor
Nicholas (with moustache only) and Count Benckendorff
Alexandra with lady in waiting in role of nurse to an invalid
But, as has been said, the parents' fatalism was a major factor in the lack of action.
Ann