...and I thought we had agreed that a correct reading of the Kasting-Williams article makes it completely clear that any ephemeral atmosphere, produced by a giant impact, capable of allowing either liquid water or liquid CO2 to exist anywhere on Mars' surface would transfer enough heat to Mars' poles to protect itself from freezing out again at the poles, even during the time of the faint early Sun.

The picture of Martian history I still stick to is one in which such a dense Noachian CO2 atmosphere did exist -- although whether it produced enough greenhouse effect to allow liquid water to exist actually on Mars' surface is still in doubt -- and that, as that dense atmosphere gradually disappeared for other reasons (impact erosion, solar wind erosion, and/or subsurface carbonate formation), its greenhouse effect was finally reduced to the point that it COULD freeze out at the poles, so that Mars' atmosphere suddenly collapsed into giant polar CO2 icecaps, which then underwent basal melting and so injected large amounts of liquid CO2 into Mars' subsurface. That, in turn, would allow your vision of Hesperian Mars -- and your gas-eruption explanations of both the giant catastrophic outflow channels and the small slope gullies -- to work perfectly, while still allowing a liquid-water related explanation of the earlier valley networks (whether that water flowed on the surface or a short distance underground).