The year 1955 was the atomic bomb as far as Octaves (and many other ancient liturgical observances) go, so it is beyond debate that ALL of the Octaves on the Kalendar as of 1911, most from antiquity, must be reestablished and continued here as part of the Current Tridentine Ordo (CTO). I would also keep the Octave of the Sacred Heart, but this can be debatable.
As one commentater here added some insightful remarks about the nature of Octaves in general, this question and other related questions beg for further discussion. Let's divide this into two considerations: 1. The nature of an Octave in general and 2. Questions arising from adapting Pian rules to restored Tridentine practices. With the Octave of St. Lawrence approaching next month (which is also the next Octave on the General Kalendar as we take a summer rest from such liturgical activity), we can use this as an example for these points.
1. The Nature of an Octave
While I believe the ordering of Octaves done by St. Pius X in 1911 was a welcome revision (more about this in part 2), St. Pius X also introduced a liturgical novelty when assigning the least important Octaves the rank of Simple. These would be all of the Octaves associated with those particular feasts of Double II class which merited an Octave. The novelty arises in creating a distinction between an Octave per se and the continuous celebration of a feast throughout eight days. Let's leave aside the Easter and Pentecost Octaves from this discussion; I believe this is a different topic and gets off track here. The Pian "Simple Octave" is in reality a duet - the feast itself and its octave day with a hole in between. Hitherto, an Octave meant exactly that, a continuous celebration of a feast for eight days with the feast day itself and its Octave meriting greater solemnity while the other six days are categorized as days within the Octave. The Pian reform would seem to "attack" the very nature of what an Octave is, and the CTO is now reconsidering whether or not to keep the "Simple Octave" in existence. This brings us to the practical application in part 2.
2. Questions arising from adapting Pian rules to restored Tridentine practice
a. Looking at the Tables of Occurrence and Concurrence from my 1854 Breviarium (i.e. pre-Pius X ranking), generic days within (i.e. Days 2-7) an Octave only supersede Simple ranked feasts. Hence, even minor Sundays per Annum take precedence, so if we look ahead to 11 August, the second day of St. Lawrence's Octave (a semidouble Office itself), the Sunday Office holds while the Octave is commemorated. This poses a question, though, that I am not entirely clear about - in post-1911 rubrics, whenever an Octave is commemorated on a Sunday, both the Dominical Preces and Athanasian Creed would be omitted at Prime, but in the Tridentine Sunday Office, those two elements are given as normative whenever the Sunday Office is prayed. The aforesaid commentater posited that an Octave would always supersede a Sunday, making our question moot, but I believe his posit to be incorrect per the tables referenced above. I am certainly in favor of the Tridentine practice of retaining the Sunday Office intact rather than "if a Double or Octave" occurs the rules change; with Double feasts superseding minor Sundays per Annum, this rule change should be moot, but it's not when 11 August is a Sunday (or 4 July, or 11 September, etc.).
b. It's in the nature of feasts to have distinguishing aspects of Octave celebration. Hence, the Tridentine rubrics already provided for keeping the Easter and Pentecost Octaves clear of any feasts; similarly, the Epiphany and Corpus Christi Octaves were cleared of all feasts save Doubles I class. The Christmas Octave, being fixed to specific Kalendar dates, functions such that any feast of nine lessons at Mattins supersedes the days within the Octave and this provides the basis for the Pian "Octaves of the Third Order" for the same treatment for the Ascension (and later Sacred Heart) Octaves. "Common Octaves" have the same precedence rules as the "Third Order Octaves" but in the post Pian Psalter, the distinction arises by using the Ferial psalms for the latter. Hence, in the restored CTO whereby festal psalmody continues throughout the days within Octaves, there is no difference in precedence or in practice between a "Third Order" vs. a "Common" Octave. So why keep both? But then it seems strange to put the Octaves of Sts. Peter & Paul, St. Lawrence, and the Ascension all on equal footing! If we were to retain the "Simple Octave", it would itself be a liturgical novelty to adopt the ferial psalmody/single nocturn Office for days within an Octave, although this is precisely what St. Pius X did to the Octave Days of St. Lawrence, Nativity of Our Lady, and the comites feasts next to Christmas. I think there is no solution save to treat all Octaves below that of the "Second Order" as the same, and modify the Pian arrangement into three categories - First Order, Second Order, and Common. The days within all Octaves would remain Semidouble in rite (save for the Monday and Tuesday of the Easter and Pentecost Octaves), so all Octaves will retain a festal Office with three nocturns at Mattins throughout their entirety. The Octave Days would be Double Major if the feast itself is a Double I Class and Double (Minor) if the feast itself is a Double II Class. In any case, Octave Days would always supersede minor Sundays, while days within the Octave would not.
c. Tridentine rubrics stipulate that days within the Octave are not to be commemorated in occurrence when a Double I or II Class occurs. The Pian system retained this, so we also retain it for all Common Octaves. This would be rare in application for an Octave of the Second Order (we will retain the commemoration of such an Octave when a Double I Class feast occurs (e.g. the Nativity of St. John the Baptist falls within the Corpus Christi Octave), and never a consideration in a First Order Octave.