"Cycling" happens when the nutrient load on the tank and the nutrient processing abilities of the tank don't match.
So, for each element you're putting in the tank, ask yourself two questions:
1) Is this element adding to the nutrient load in the tank?
2) Is this element adding to the nutrient processing capabilities of the tank?
Some things are obvious, but others aren't. For instance, the "cycled" live rock from your 90g. Surely it has bacteria living on it, so it's increasing the nutrient processing capabilities of the new tank. But, is it loaded with sediment and deposits? If you blast a powerhead at the rock from close range, does the water get cloudy or stay clear? It's possible for "cycled" rock from an established tank to be very dirty, such that moving it to a new tank DOES cause nutrient problems, thanks to the sediment and detritus accumulation getting stirred up into the water.
Also, might make sense to take a moment and evaluate your motives. Cycling is a natural part of setting up a new tank and a few extra weeks isn't much compared to years of enjoyment once things have settled down. The only times I've purposely tried to "rush" or avoid a cycle in a new tank was when I HAD to - i.e. when I upgraded from a smaller tank to a larger one, and needed to transfer livestock immediately.