I'm not gonna pursue this tangent. It's exactly what you posted except starting at a different point in the rotation to be more legible.
More relevant to the discussion, injecting the F to each IDC (or anywhere else in the rotation tbh):
H IDCF P TTT H TTT
P IDCF H TTT P TTT
Is still leading until you hit a 2.3s GCD (+200 skill speed, supposedly, or a combo of less skill speed and team buffs; IIRC a scholar has a SS buff).
At the 2.3s GCD, the other adjustment you mentioned leads (although I would use the F and P together, rather than H and F, but it doesn't matter):
HF IDC P TTT HF TTT
P IDC HF TTT P TTT
Note that it is generally similar to, but does slightly more damage than:
HFP IDC TTT
HFP TTT IDC
HFP TTT TTT
Because of better buff timing.
Edit:
So the real question here is how realistic is it to hit a 2.3s GCD.


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