Exact climate data from the past
This all looks very impressive. But I have an easier method for determining climatic conditions of the past. Look what grew where and when. When whalers were buried in the dirt in Spitzbergen at some time in the past, it must have been warmer there. When there were extended and lush forests in Greenland 1000 years ago, it must have been warmer than today. When Romans have cultivated red wine in northern England 2000 years ago, it must have been warmer than now. There are plenty of other hints like these. Maybe a way to calibrate your more technical assumptions.