You’re comparison doesn’t work very well. The Northern Hemisphere may not be at full heat by June 22, but neither does it take until June 22 for the Earth to begin heating up. According to what you write, we may not yet be in the coldest part of an ice age, but it would be starting to cool off. If such cycles were SO slow to initiate, they would simply blend together.
That's a non sequitur. I was talking about peaks; of course there is a warming period before the peak. The energy delivered by solar radiation in the Northern Hemisphere increases before the Jun 22 peak, the resulting heat of the Earth increases before the Aug/Sep peak. Even on a daily basis, the warmest part of the day is not always at Noon, but usually later in the afternoon.
The ice ages cycles are slow, but clearly have not blended together to an average. Every 100,000 years or so, we get 10-20,000 years of non-ice age.
Cycles of different periods do blend together most of the time, but regardless of the variation in the period, eventually the cycles will all hit a peak (or low) at the ame time.