Wye-delta starting to reduce inrush current is essentially a misconception that satisfies a poorly defined requirement from the utility in the cheapest possible manner. The reality is, there is
ALWAYS a "transition spike" in an open transition starting scheme. Sometimes it is worse than others, but in all cases, the spike current magnitude is the same, if not worse, that the Across-the-Line starting current. Usually though, the duration is much shorter, so the utility systems can accept it without as much negative effect.
What makes the magnitude greater or lesser from one application to another is a set of complex interactions of timing, phase angles, motor flux penetration and load inertia. It is VERY difficult to accurately predict the correct timing, being that it is the only one of the parameters that you can control. Sometimes you get lucky, sometimes you don't. Sounds like you didn't. The best solution is to abandon the "lie" that is wye-delta starting and use a soft starter; smooth acceleration and no transition.
If that is not an option, you can play with timing all you want, but if it is as bad as you say, it will not likely have much affect all by itself. I would start by "rolling" the contactors for the 3 main leads. Rolling means that you swap position of the conductors; but not phase order, i.e. A to B, B to C, C to A. This shifts the phase angle at the moment of transition and can often lessen the severity of the transition spike, making it more amenable to changing the timing.
To learn more about this, read these white papers:
Richard Nailen paper on switching transients
Robert Woodall paper on Wye-Delta starting transients