The shift from 41 ka cycles to the current ~100 ka maybe cycle is due to changes in the internal harmonics of the global ocean heat transfer. Bold statement, right?
Looking at the first chart again, the x-axis is scaled to 23ka years and shift to align with some of the more interesting peaks. The precession frequency is not exact and the decay frequency or internal harmonics of the oceans are not exactly tuned to the precessional frequency. The 4.3ka recurrent frequency of the ocean oscillations from precessional perturbation is not a perfect "fifth", it is a little out of tune. The Oceans also have a ~5.8ka decay from the 41ka obliquity perturbations indicating they decay well before that next perturbations. The oceans are current tuned to ~21.5ka cycles which drift allows to synchronize either with precession or with every second or third obliquity cycle.
Showing why there is a new tuning since ~800ka years ago is a challenge, but the precessional cycle has been in charge in the distant past.
Timing is everything in nonlinear dynamics, whether it is a golf swing or paleo climate.