Just for discussion purposes, since Wye-Delta starting requires, as the name implies, a switching of the motor windings from one connection (wye) to another (delta). Switching the motor from wye to delta by the open transition method allows it to be completely disconnected from the power source for a brief time period before being reconnected delta.
So technically there are 6 CCC in the conduit and invokes Table 310.15(C)(1) Adjustment Factors for More Than Three Current-Carrying Conductors, the 6 conductors are never carrying current at the same time, only 3 at a time.
Maybe a work around, not requiring the table ?
In reality, I've not used a Y-D starter in many years, since VFD's are relatively cheap, but it was something that crossed my mind.