> Do any feel-like estimates take cloud cover into consideration?

No, usually not, because they're usually just simple toys combining a heat index and wind chill scale.

There _is_ an official metric used for estimating heat stress that accounts for cloud cover - the Wet-bulb Globe Temperature (e.g. https://www.weather.gov/tsa/wbgt). This is what is used, for instance, in literature analyzing the impact that future climate change might have on heat stress and mortality risk during heat waves. It's also used by some professional sports programs to monitor risk for crowds and athletes, as well as commonly used by OSHA and other regulatory agencies looking at worker exposure to heat hazards.