I am not saying that you should mix rites, only use the 1962 missal to give some hints. The novus ordo isn’t exactly clear when it comes to the direction of the celebrant, so a lot is left to guess work.
I think the current missal is perfectly clear and nothing at all is left to guess work if one reads the rubrics -
If a priest celebrates ‘ad orientem’:
*he starts the Liturgy of the Eucharist stans ad altare, ‘standing at the altar’
and he would would turn:
*for the ‘Orate fratres’
(stans … in medio altaris, versus ad populum,…dicit: Orate fratres…)
*for the ‘Pax Domini…’
(Sacerdos, ad populum conversus…subdit: Pax Domini…)
*for the ‘Ecce Agnus Dei’
(Sacerdos…ad populum versus,…dicit: Ecce…)
*then he would turn to face the altar for his communion
(Et sacerdos, ad altare versus, secreto dicit:
Corpus christi custodiat…
Et reverenter sumit Corpus Christi.)
The current Missal’s rubrics clearly and explicitly provide for Mass ‘ad orientem’.
However, a priest is also allowed to celebrate facing the people. (I suppose that when he does so he is technically both ‘versus ad populum’ [turned towards the people] and ‘ad altare versus’ ‘turned towards the altar’] at the same time.)