Didn't all those years at Uni teach me nuffin' ? When in doubt always go to the primary sources. In this case that would be Yoga Mala.
'....do Rechaka and Puraka as fully and as much as possible'.
Sri K patatbhi Jois. Yoga Mala p177 ( and elsewhere ).
In fact he says the same thing on pretty much every page of Yoga Mala, Or he might say this...
' ....while in the state, do Puraka and Rechka , slowly and deeply as much as possible'. p68 (and elsewhere).
SKPJ is saying, again and again, long slow breaths....... lots of them.
He stresses engaging bandhas again and again .
He tells you to stay in Sarvangasana
'.... five, ten, fifteen even thirty minutes doing rechaka and puraka deeply.' p 104
And in Shirshasana
'... during which rechaka and puaka should be done slowly and as many times as possible.' p116
In defense it's not all my fault : ) I learnt from books and DVDs where the practice is squeezed into an hour to an hour and a half. Even in Lino's book supposedly authorised he tells you to take five breaths in most of the asana, though he does say 25 in handstand and headstand. And of course when I would read Yoga Mal,a I was usually looking at how to get in and out of an asana and didn't pay enough attention to the breath.
Oh and another thing, Guruji refers to Janu Sirasana as sometimes being called Maha Mudra, given there's A, B and C we spend quite a while there. He also stresses the importance of the order of asanas.
Maybe some of the emphasis has changed over time, but in Yoga Mala it's very close to Vinyasa Krama. The only difference seems to be the range of asanas, sub-routines and sequences. In Ashtanga it's a fixed system in Vinyasa Krama it's a fuller broader range of asanas and routines that can be adapted to the needs of individual practitioners.
I'm wondering if when Krishnamacharya was teaching at the Mysore palace he was teaching a fixed system, the students having to adapt to the system. After he left and was teaching individual students the focus perhaps shifted to adapting the practice to individual. Just a thought.