“Adequate atmospheric data to attempt to predict future temperatures have only been acquired during the last 40 years.”
Thermometer measurements go back to 1850, and, in some cases, even to 1753. Prior to that, proxies are used to go back thousands or hundreds of thousands of years. The most accurate proxy is the ice core, whereby they measure the oxygen isotope ¹⁸O.
Regarding the efficiency of climate modeling, if we dig a little bit in what scientists spend their time on, we find that climate models fairly describe past observations (i.e. hindcasting) and are reliable to estimate future trends (see, for instance, Zeke Hausfather et al. or Jouni Räisänen).
Examples include: James Risbey et al. (on global surface warming for ENSO phase), Michael Mann et al. (on global and hemispheric mean temperature and human influence), Julienne Stroeve et al. (on retreat and thinning of the Arctic sea ice cover) or L. Harvey (on the response of mean annual temperature and precipitation to CO2 radiative forcing). Even the oldest climate model seems to be quite accurate.
Regarding your comments on the greenhouse effect, it was not my intention in this article to provide a full explanation of its physical dynamics. Your suggestion is perhaps a good idea for a topic of a new article.