Stern never used a discount rate as low as 1 or 1.4. He used a standard eta, and a low delta - which ended up with a discount rate in the neighborhood of  4.6% which was slightly above the rate of the U.S. ten year long bond at the time. If you don't mind, I will link to a Quiggin blog post which is much less technical than the two Quiggin pieces you quoted, but explains the confusion:

Given eta = 1, the discount rate is equal to the rate of growth of consumption per person, plus 0.1. A reasonable estimate for the growth rate is 2 per cent, so Stern would have a real discount rate of 2.1 per cent. Allowing for 2.5 per cent inflation, that's equal to a nominal rate of 4.6 per cent. The US 10-year bond rate, probably the most directly comparable market rate, is currently 4.44 per cent; a bit above its long-run average in real terms. So, Stern's approach produces a discount rate a little above the real bond rate.

Your larger point about Stern undervaluing the damage from climate chaos is quite right.