I am fairly confident that the date of "August" for Sybil's death is wrong (I used the tenessee amendment as the date... but that doesn't actually occur until after 3.08).
However, I cannot work out Sybil's actual D.O.B other than it's before July. Or possibly April.
Her 17th birthday occurs before July, as she's presented to "their majesties" in June (and Violet mentions June too, when she refers to the riot; the episode starts with the family's return in July, after Sybil's debut) but the script says that Sybil is already 17 at the sinking of the Titanic in April.
If April is right, then 3x01 - 3x05 are set between Feb/March and April.