"All census records [1790 – 1840] prior to the 1850 census ONLY listed the head of household; whether male or female.
. . .
NO place of birth was stated – city, state, or country"
--There are exceptions. Some of the Maine enumerations for 1810 stated County of birth of the head of household.
"NO occupation was stated"
--There are exceptions. The 1810 enumeration for Jefferson Co., (West) Virginia gave occupations, for example.
"NO race was stated [but assume “white”]"
--This is just incorrect. The 1790 through 1840 enumerations have some 'racial' designations such as 'black', 'free black', non-taxed Indians. Each enumeration varies as to category and whether age-ranges are given. The enumerations that count "slaves" should not be assumed to be listing just what the enumerator might perceive as African-Americans. And the enumerators' perceptions may or may not be the same as what a person today might say. Since there actually is no such thing as "race," and a variety of intermingling of various geographic ancestries' blood took place, physical appearance was and is not a very good guide to what those ancestries might be.