If I understand correctly, your argument in particular suggests that it's the environmentally-mediated increase in IQ that might have enabled the rise of civilization (in this interglacial period).

This doesn't seem to be all that Douglas_Reay is arguing. There's also an aspect to his argument of the right environmental aspects being available for an extended period of time, along with the slow development of the right technologies for society to take off. See in particular these two paragraphs:

Good grain storage seems to have developed incrementally starting with crude stone silo pit designs in 9500 BCE, and progressing by 6000 BCE to customised buildings with raised floors and sealed ceramic containers which could store 80 tons of wheat in good condition for 4 years or more. (Earthenware ceramics date to 25,000 BCE and earlier, though the potter's wheel, useful for mass production of regular storage vessels, does date to the Ubaid period.)

The main key to the timing of the transition from village to city seems to have been not human technology but the confluence of climate and biology. Jared Diamond points the finger at the geography of the region - the fertile crescent farmers had access to a wider variety of grains than anywhere else in the world because that area links and has access to the species of three major land masses. The Mediterranean climate has a long dry season with a short period of rain, which made it ideal for growing grains (which are much easier to store for several years than, for instance bananas). And everything kicked off when the climate stabilised after the most recent ice age ended about 12,000 years ago.