Oh dear...
You talk of changes to the obliquity over the last 2000 years, well, I'll attach a figure charting temperature trends for the past 65 million years (Ma).
This figure is from a paper published on the "Proceedings of the National Academy of Sciences of the United States of America" website
It's probably not going to change your mind, but here is a link to the document:
https://www.pnas.org/content/115/52/13288
Here's an excerpt from the abstract to the article:
Here, we quantitatively assess the similarity of future projected climate states to these six geohistorical benchmarks using simulations from the Hadley Centre Coupled Model Version 3 (HadCM3), the Goddard Institute for Space Studies Model E2-R (GISS), and the Community Climate System Model, Versions 3 and 4 (CCSM) Earth system models. Under the Representative Concentration Pathway 8.5 (RCP8.5) emission scenario, by 2030 CE, future climates most closely resemble Mid-Pliocene climates, and by 2150 CE, they most closely resemble Eocene climates. Under RCP4.5, climate stabilizes at Pliocene-like conditions by 2040 CE. Pliocene-like and Eocene-like climates emerge first in continental interiors and then expand outward. Geologically novel climates are uncommon in RCP4.5 (<1%) but reach 8.7% of the globe under RCP8.5, characterized by high temperatures and precipitation. Hence, RCP4.5 is roughly equivalent to stabilizing at Pliocene-like climates, while unmitigated emission trajectories, such as RCP8.5, are similar to reversing millions of years of long-term cooling on the scale of a few human generations. Both the emergence of geologically novel climates and the rapid reversion to Eocene-like climates may be outside the range of evolutionary adaptive capacity.