First things first: There's nothing per se wrong in science with answering "We don't know" to a vexing problem. This might well be one of those cases.
The question you are asking was asked by Imbrie and Imbrie in 1980. The problem you have noticed (a very strong interglacial despite low Milankovitch forcing) is now known as the "stage 11 problem", and this appears to be closely associated with the transition from a ~41000 year glacial cycle to the ~100000 year cycle we have seen for the last 900000 years.
Why "stage 11"? This is a reference to the concept of Marine Isotope Stages, depicted below. The Marine Isotope Stages refer to the abundance of oxygen 18 relative to oxygen 16. Water made of two protons (hydrogen) and one oxygen 16 atom evaporate more readily than does the slightly heavier water centered on an oxygen 18 atom. This makes the oxygen 18 levels in oceanic deposits a very nice proxy for climate.
Three key transitions can be seen in the above graph. The glacial cycle started to change from a ~41000 year period to a ~100000 year period a bit less than one million years ago. The second transition occurred after MIS 17 when glacials shifted to being more extreme. The third transition, the one that you noticed, occurred after MIS 12 when interglacials shifted to being more extreme. This latter shift is the core of the "stage 11 problem".
The key issue with explaining the observed ~100000 year cycle is that the Milankovitch forcings for a 100000 cycle are rather low while the Milankovitch forcings for a ~41000 year cycle are very strong. The stage 11 problem gets at the very heart of the 100000 problem because stages 12 and 11, which mark an extremely large swing in climate, occurred when Milankovitch forcings were very low. One non-solution of this stage 11 problem is that the onset of stage 11 (or possibly the onset of the preceding stage 12) represents when the 100000 year cycle finally took full control. This is essentially the argument made by Berger and Wefer.
So, rhetorically, what did cause this shift from a glacial cycle of ~41000 years to ~100000 years, and why did it take half a million years for this transition to become complete? A partial explanation by Abe-Ouchi et al. is that something happened between 0.4 and 1.0 million years ago that enabled hysteresis loops. Instead of disappearing on a 41000 cycle, ice instead built up to such thick levels that all of the ice didn't melt at what would have ended a 41000 year glaciation. Once that happened, it wasn't much of a jump to survive two 41000 year cycles. But by then the ice had become so very thick that all that was needed was a mild forcing from warming to make the ice melt catastrophically.
This still falls in the "and then magic happens" category. One very plausible hypothesis that has gainied a lot of traction (e.g., Bintanja and Van de Wal) is that those massive ice sheets eventually pushed the built-up regolith from the 200+ million years since the previous ice age (the Karoo) either out to sea in the north or in huge piles of glacial drift to the south.
The initial glaciation events of the current ice age that started about 2.6 million years ago were rather weak in part because regolith makes for a rather nice ice lubricant. Those comparatively weak glaciation events continued for the next 1.6 million years, at a 41000 year interval. Much of the regolith had been pushed out of the way by a million years ago. While regolith is slippery (to ice), bare rock is anything but. This stickiness enabled ice to build up to the extent that those hysteresis loops could start to form, sporadically. It took another half a million years for the transition from a purely Milankovitch-driven 41000 year cycle to a Milankovitch+hysteresis 100000 year cycle.
Imbrie, John, and John Z. Imbrie. "Modeling the climatic response to orbital variations." Science 207, no. 4434 (1980): 943-953.
Berger, W. H., and G. Wefer. "On the dynamics of the ice ages: stage-11 paradox, mid-Brunhes climate shift, and 100-ky cycle." GEOPHYSICAL MONOGRAPH-AMERICAN GEOPHYSICAL UNION 137 (2003): 41-60.
Abe-Ouchi, Ayako, Fuyuki Saito, Kenji Kawamura, Maureen E. Raymo, Jun’ichi Okuno, Kunio Takahashi, and Heinz Blatter. "Insolation-driven 100,000-year glacial cycles and hysteresis of ice-sheet volume." Nature 500, no. 7461 (2013): 190.
Bintanja, R., and R. S. W. Van de Wal. "North American ice-sheet dynamics and the onset of 100,000-year glacial cycles." Nature 454, no. 7206 (2008): 869.