The two Asteroid strikes at 35.3 million and 35.7 million years ago never left a signature in the Temperature record within the resolution of the data available of 15,000 years.
The glaciers in Antarctica started forming about 42 million years ago and the significant glaciation did not start until 33.6 million years ago.
So, the Asteroid strikes did not impact the long-term climate and a lag of 2 million years is not possible.
In terms of this study, trying to use ancient soils to estimate CO2 in the past - this method has huge errors/variability and produces Zero ppm estimates very often (ie no plants, no life). The author of the study, Royer, is desperate to rewrite the historical CO2 estimates so that it matches the historical temperature records better. This is just another example.
Sorry, when I saw Royer’s name, I assumed he was involved in this, but I guess he wasn’t. The method, however, is not reliable.
The various figures you mention assume there is no argument about their accuracy, nor for that matter the figures I mntioned. So perhaps the boloid events are closer to some other measured events.
You mention that glaciation in Antarctica started about 42 mya. Other comments refer to later figures, although those could refer to well developed glaciation, not the beginning. Interesting factoid: If you look at the sea mounts leading off from the Hawaii hot spot, you will see that at first they trend east north east, then there is a sharp movement more directly to the north. I believe the age given for this directional change was around 43 mya. So the question, if my memory and their figures are correct, did some major event start the Antarctic glaciacion?
I really hope that more interdisciplinary work will be done on identifying and dating all these different major events—boloid, volcanic, seismic, etc. Only then will it be possible to develop the most accurate theories and come to conclusions that most people will accept.