It is an interesting theory.
But I think that if normal acceleration due to the actually curved path of a level flight was noticeable (even eastbound along the ecuator), it would be corrected for by the computers (either ADIRUs or ELACs, SECs). I think the ADIRUs aldready take it into account in order to display attitude correctly.
Otherwise, all what they explain in the FCOMs would be rubish. The airplane would never be path stable, as they claim.
But maybe you have a point, because what the FCOMs explain about the roll axis, for instance, is rubish, in my opinion. So why would it not enter in phugoids? I would really love to do some "flight testing"...
Mach number cannot be correctly displayed if pitots are blocked, but if you have IAS readings (incorrect) you will have TAS and Mach readings, too (incorrect, naturally). And I guess that the two "frozen" ADRs rejected the good one? So you did see all readings (incorrect) without warnings nor red flags.
When studiying UNRELIABLE SPEED procedure, it seems that the memory items "when safety of flight is affected" are just for shortly after take off, or during final approach or go around. But they are equally valid at cruising level when you are half asleep. Disconnecting the A/THR is vital but, for some reason, is the most frequently missed item when doing this drill.
Regarding to the mach measurement, I know the equations and relationships among TAS, EAS, FL, OAT, Mach... But I don't remember/understand well how Mach is computed if IAS has a compressibility error proportional to the mach number itself. I guess that in the computations, somehow this effect is "gone out" of the equations?
Cheers