Bismillah
as salam alykom
Ok Dan on this very interesting topic, Jazakum Allah khairan for making me search on it.
I check the meanings first, on the site of ibn Baz, he quoted the same Ayahs i did. But to correct something, he said that basically Qiyam and Tahajud are the same, which is logical according to the Ayahs. Both are performed on a voluntary basis after Esha till Fajr.
So we cannt really make one better than the other.
As for the number issue, I also searched on a credible site and found that the only number proved after the Messenger salla Allah a`lyhee wa sallam is as u quoted in the hadeeth of Aisha. However, as Ibn hijr mentioned in his book Alfath, he said that there are other options taken after the Sahaba and that this issue is somewhat flexible. I mean there is not harm if u take any of the options (this is exactly what was written in Arabic:
Taraweeh
He cited other numbers like:
11, 21, 23, 39, 41,49.
Actually if u think about it logically, Allah in Quran say:
"They used to sleep but little by night [invoking their Lord (Allah) and praying, with fear and hope]." (Quran 51:15)
Now let us look here at this Ayah, Allah Is describing a group of people who used to sleep only a little time during the night, what did they do other wise? of course pray. One who spends most of the time not sleeping shall not of cours restrict him/her self for only 11 Raka. But rather shall increase.
In fact, this makes it logical that a certain number was not decided by the Messenger in order to leave it to the ability, circumstances, capacity of each individual.
Jazakum Allah khairan for making me do this excercise.
wa Allah u a`lam.