Calculation of pressure change need to induce ice-age cycle

In my previous post I suggested that the addition of gases to the atmosphere from volcanic activity could have increased the atmospheric pressure and that would have changed  global temperature giving us the current warm interglacial.
Today I thought it was worth putting some figures on that (thanks to Will Janoschka for the question that prompted it). And here it is: I don’t claim to be doing anything other than using the approximation given by Niklov and Zeller 

Ts/Tgb = exp(.233Ps^0.0651 + 0.00154Ps^.385)

Where Ts is surface temperature (C), Tgb is earth’s “grey body temperature” which I treat just as a constant as given in the paper (154.3C), and Ps is surface pressure of around 100,000 pascals.

This suggests that in the ice ages, the 8C lower temperature could be explained by a 30% drop in pressure. That is equivalent today of an altitude rise of 3200m. For us living in Scotland where our highest mountain (Ben Nevis) is around 1300m that sounds high.
But worldwide Peru’s La Rinconada is at 5100m, China’s Qinghai is at 4870m, India’s  Korzok at 4570m and Chile, Nepal, Bolivia, Argentina, Afghanistan, Jyrgystan, Bhutan, Tajikistan, United States, Mexico, Ethiopia, Columbia, Ecador and Turkey all have towns higher than 3200m and Bolivia’s capital La Paz is higer at 3640m. And given we humans have towns up to 2000m higher than the height for the required pressure drop, we could occupy land up to at least 2000m with a 30% drop in atmospheric pressure.
Only 8 out of around 180 countries have capital cities above this 3200m height, so most of the densest populated areas today would still be habitable with a 30% lower air pressure.
Data
The approximation suggest the following change in global temperature with changes in global pressure:

Can require pressure change be explained by drier conditions in ice-age?
Total water vapour is of the order of 0.5%. So at worst, going from 0% to 100% humidity is only going to equate to around a 0.1C change in global temperature.
Can the weight of added CO2 explain the 8C change?

As above a 5,000ppm change in weight of atmosphere equates to 0.1C, so the 100ppm change in CO2  results in an order of magnitude smaller change in temperature. It isn’t even worth me calculating as the answer is clearly no.
Birds – a testable prediction?
It is reasonable to say that if air pressure caused the lower temperature in the ice-age then birds that cannot fly above 3200m (due to the lower lift) would not be present. In other words, we can disprove this theory if we can find a bird that cannot fly above 3200m and has not changed significantly through the ice-ages.
(Initially I was thinking about larger birds, but then I remembered a film of geese flying above … I think it was the Himalayas … so that doesn’t look very helpful as even today some of our larger birds fly well above 3200m. The bigger problem may be take-off!).
Looking at this site: ScienceDaily I find:

[in the ice-age] the mixtures of birds that lived together were different from anywhere in the world today. Birds exotic to Britain, such as species normally expected in the tundra to the north (like skuas, and hawk owls), the Mediterranean to the South (like alpine swifts) or the Eastern steppes (like demoiselle cranes and long-legged buzzards) lived together with birds expected in the region today (such as grey herons and wood pigeons).

John Stewart continued, “It is clear the birds of the time of Neanderthals have changed in a way that is almost as dramatic as the change we have seen in mammals

I’ve no idea how to interpret that!